# Journal of Statistical Theory and Applications

349 articles

**Research Article**

## The gamma extended Weibull family of distributions

Abraao D.C. Nascimento, Marcelo Bourguignon, Luz M. Zea, Manoel Santos-Neto, Rodrigo B. Silva, Gauss M. Cordeiro

Pages: 1 - 16

We introduce a new family of distributions called the gamma extended Weibull family. The proposed family includes several well-known models as special cases and defines at least seventeen new special models. Structural properties of this family are studied. Additionally, the maximum likelihood method...

**Research Article**

## Characterizations of Distributions Based on Properties of Exponentially Shifted Records

M. Ahsanullah, S.M. Ananjevskii, V.B. Nevzorov

Pages: 1 - 7

**Research Article**

## Concomitants of Dual Generalized Order Statistics from Morgenstern Type Bivariate Generalized Exponential Distribution

Saeid Tahmasebi, Ali Akbar Jafari, Mahmoud Afshari

Pages: 1 - 12

[9] introduced the concept of dual generalized order statistics (dgos) that enables a common approach to descending ordered random variables like reversed order statistics and lower record values. In this paper, we have obtained probability density function (pdf) of r-th, and the joint pdf of r-th and...

**Research Article**

## On Marshall-Olkin Extended Weibull Distribution

Hanan Haj Ahmad, Omar M. Bdair, M. Ahsanullah

Pages: 1 - 17

In this paper, we introduce a new form of distributions called ”Marshall-Olkin Extended Weibull distribution” MOEW. We study some of its structural properties and the shape of its hazard rate function. We provide some methods of point estimation for the unknown parameters and discuss its asymptotic properties....

**Review Article**

## Preservation of Classes of Discrete Distributions Under Reliability Operations

I. Elbatal, M. Ahsanullah

Pages: 1 - 10

In this paper we consider some widely utilized classes of discrete distributions and aim to provide a systematic overview about their preservation under convolution. This paper will serve as a detailed reference for the study and applications of the preservation of the discrete NBU(2), NBUCA classes...

**Research Article**

## A New Zero-Truncated Version of the Poisson Burr XII Distribution: Characterizations and Properties

Haitham M. Yousof, Mohammad Ahsanullah, Mohamed G. Khalil

Pages: 1 - 11

In this work, a new four-parameter zero-truncated Poisson Topp Leone Burr XII distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary and incomplete moments, residual and reversed residual life functions, generating functions, order statistics...

**Research Article**

## Bayesian Estimation of the Scale Parameter of the Marshall-Olkin Exponential Distribution under Progressively Type-II Censored Samples

Mukhtar M. Salah

Pages: 1 - 14

This paper studies the Bayes estimator, the maximum likelihood estimator and the approximate likelihood estimator of the scale parameter for the Marshall-Olkin exponential distribution under the progressive type-II censored sample. All the estimators, Bayes estimator, maximum likelihood estimator and...

**Research Article**

## Dynamic Systems with Baseline Exponential Distribution Based on Sequential Order Statistics Under a Power Trend for Hazard Rates

Majid Hashempour, Mahdi Doostparast

Pages: 1 - 9

This paper deals with analyzing dynamic engineering systems consisting of independent components. The failure of a components causes more load on the surviving components. This property is modeled by a power trend conditionally proportional hazard rates. For modeling system lifetimes, the theory of sequential...

**Research Article**

## Similarity Measure Based on the Belief Function Theory: Application in a Decision-Making Process

M. Khalaj, F. Khalaj

Pages: 1 - 10

This study considers a new aspect of the belief function theory to define a belief set, which is characterized by truth, uncertainty and falsity belief degrees as a 3D vector representation. Then, based on the implication of a belief set, one of the similarity measures (i.e., Cosine, Jaccard and Dice)...

**Research Article**

## The Exponentiated Kumaraswamy Inverse Weibull Distribution with Application in Survival Analysis

J.A. Rodrigues, A.P.C.M. Silva, G.G. Hamedani

Pages: 8 - 24

In this paper, a new distribution called the exponentiated Kumaraswamy inverse Weibull is proposed. This dis- tribution includes as special cases the inverse exponential, inverseWeibull, inverse Rayleigh and exponentiated inverse Weibull distributions. We study the main properties of this distribution,...

**Research Article**

## A Stochastic Approach in Modeling of Regional Atmospheric *CO*_{2} in the United States

Doo Young Kim, Chris P. Tsokos

Pages: 10 - 20

Global warming is a function of two main contributable entities in the atmosphere, carbon dioxide, and atmospheric temperature. The objective of this study is to develop a statistical model using actual fossil fuel carbon dioxide emissions data from the United States to predict relative probability of...

**Research Article**

## Characterizations of Certain Recently Introduced Distributions

G.G. Hamedani

Pages: 11 - 20

Various characterizations of the Beta Weibull Geometric distribution of Bidram et al. (2011), the New Generalized Exponential distribution of Bidram et al. (2012), and the Gamma Exponentiated Weibull distribution of Pinho et al. (2012) are presented. These characterizations are based on: (i) a simple...

**Research Article**

## Restricted Empirical Likelihood Estimation for Time Series Autoregressive Models

Mahdieh Bayati, S.K. Ghoreishi, Jingjing Wu

Pages: 11 - 20

In this paper, we first illustrate the restricted empirical likelihood function, as an alternative to the usual empirical likelihood. Then, we use this quasi-empirical likelihood function as a basis for Bayesian analysis of AR(r) time series models. The efficiency of both the posterior computation algorithm,...

**Research Article**

## A Family of Ratio Estimators in Stratified Random Sampling Utilizing Auxiliary Attribute Along Side the Nonresponse Issue

Usman Shahzad, Muhammad Hanif, Nursel Koyuncu, A. V. Garcia Luengo

Pages: 12 - 25

This article proposes some estimators based on an adaptation of the estimators developed by Bahl and Tuteja [1], Diana [2], Koyuncu and Kadilar [3], Koyuncu and Kadilar [4], Shabbir and Gupta [5], and Koyuncu [6] utilizing available supplementry attributes. Further, a new family of estimators is also...

**Research Article**

## Assessment of Cpm in the presence of measurement errors

Amit K. Baral, M.Z. Anis

Pages: 13 - 27

With the advent of Taguchi’s loss function, the concept of target and sticking to the target to achieve better process performance has become widely accepted. In practice, while estimating process performance, the gauge measurement error is not taken into consideration. In the real world scenario this...

**Research Article**

## Results on Cumulative Measure of Inaccuracy in Record Values

Saeid Tahmasebi, Ahmad Nezakati, Safeih Daneshi

Pages: 15 - 28

In this paper, we propose cumulative measure of inaccuracy in lower record values and study characterization results in case of dynamic cumulative inaccuracy. We also discuss some properties of the proposed measures. Finally, we study a problem of estimating the cumulative measure of inaccuracy by means...

**Research Article**

## A Note on a Characterization of Gompertz-Verhulst Distribution

M. Ahsanullah, M. Shakil, B.M. Golam Kibria

Pages: 17 - 26

Characterization of a probability distribution plays an important role in probability and statistics. This paper considers a new characterization of Gompertz-Verhulst distribution. It is hoped that the findings of the paper will be useful for researchers in different fields of applied sciences.

**Research Article**

## Characterizations of the Generalized Beta-generated family of distributions

G.G. Hamedani, V. Mameli

Pages: 18 - 25

Several characterizations of Generalized Beta-generated family of distributions, introduced by Alexander et al. (2012), are presented, giving special emphasis to the Kumaraswamy skew-normal distribution and the Beta skew-normal distribution, special cases of this family. These characterizations are based...

**Research Article**

## On the Generalized Hill Process for Small Parameters and Applications

Gane Samb Lo, El Hadji Deme, Aliou Diop

Pages: 21 - 38

**Research Article**

## Some Applications of Near-Order Statistics in Two-Parameter Exponential Distribution

Masoumeh Akbari, Mahboubeh Akbari

Pages: 21 - 27

In this paper, some characterization results for exponential distribution are established. The results are concluded in terms of number of observations near of order statistics. It is shown that its probability mass function and its first moment can characterize the exponential distribution. Also, an...

**Research Article**

## A Robust High-Dimensional Estimation of Multinomial Mixture Models

Azam Sabbaghi, Farzad Eskandari, Hamid Reza Navabpoor

Pages: 21 - 32

In this paper, we are concerned with a robustifying high-dimensional (RHD) structured estimation in finite mixture of multinomial models. This method has been used in many applications that often involve outliers and data corruption. Thus, we introduce a class of the multinomial logistic mixture models...

**Research Article**

## Parameter Estimation in Gamma Mixture Model using Normal-based Approximation

R. Vani Lakshmi, V.S. Vaidyanathan

Pages: 25 - 35

Gamma mixture models have wide applications in hydrology, finance and reliability. Parameter estimation in this class of models is a challenging task owing to the complexity associated with the model structure. In this paper, a novel approach is proposed to estimate the parameters of Gamma mixture models...

**Research Article**

## An Efficient Estimation Procedure in Two-Occasion Successive Sampling

G.N. Singh, A.K. Singh

Pages: 26 - 37

In this paper an efficient estimation procedure to estimate the current population mean in two-occasion successive sampling has been developed. An exponential regression type estimator of current population mean is proposed and corresponding optimum replacement strategy has been suggested. The superiority...

**Research Article**

## Interval Estimation of the Overlapping Coefficient of Two Exponential Distributions

Sibil Jose, Seemon Thomas, Thomas Mathew

Pages: 26 - 32

For the overlapping coefficient between two one-parameter or two-parameter exponential distributions, confidence intervals are developed using generalized pivotal quantities. The accuracy of the proposed solutions are assessed using estimated coverage probabilities, and are also compared with other approximate...

**Research Article**

## Stochastic Comparisons of Residual Entropy of Order Statistics and Some Characterization Results

Ramesh C. Gupta, H.C. Taneja, Richa Thapliyal

Pages: 27 - 37

In this paper, we have presented some results for the residual and past entropies of order statistics. Results on the stochastic comparisons based on residual entropy of order statistics are presented. Characterization results for these dynamic entropies based on the sufficient condition for the uniqueness...

**Research Article**

## A generalization of Tukey’s g-h family of distributions

J.A. Jiménez, V. Arunachalam, G.M. Serna

Pages: 28 - 44

A new class of distribution function based on the symmetric densities is introduced, these transformations also produce nonnormal distributions and its pdf and cd f can be expressed in parametric form. This class of distributions depend on the two parameters, namely g and h which controls the skewness...

**Research Article**

## On a Class of Almost Unbiased Ratio Type Estimators

A.K.P.C. Swain, Priyaranjan Dash

Pages: 28 - 35

In sample surveys ratio estimator has found extensive applications to obtain more precise estimators of the population ratio, population mean, and population total of the study variable in the presence of auxiliary information, when the study variable is positively correlated with the auxiliary variable....

**Research Article**

## LINEX K-Means: Clustering by an Asymmetric Dissimilarity Measure

Narges Ahmadzadehgoli, Adel Mohammadpour, Mohammad Hassan Behzadi

Pages: 29 - 38

Clustering is a well-known approach in data mining, which is used to separate data without being labeled. Some clustering methods are more popular such as the k-means. In all clustering techniques, the cluster centers must be found that help to determine which object is belonged to which cluster by measuring...

**Research Article**

## Discrete Additive Weibull Geometric Distribution

K. Jayakumar, M. Girish Babu

Pages: 33 - 45

Discretizing a continuous distribution has received much attention among researchers recently. Discrete analogue of the well-known continuous distributions such as Normal, Exponential, Weibull, Laplace, Rayleigh, and so on, are available in the literature. In this paper, we introduce a discrete version...

**Research Article**

## Statistical Properties and Different Estimation Procedures of Poisson–Lindley Distribution

Mohammed Amine Meraou, Mohammad Z. Raqab

Pages: 33 - 45

In this paper, we propose a new class of distributions by compounding Lindley distributed random variates with the number of variates being zero-truncated Poisson distribution. This model is called a compound zero-truncated Poisson–Lindley distribution with two parameters. Different statistical properties...

**Research Article**

## EM Algorithm and Positive Quadrant Dependence in the context of Multi-State Stress-Strength Model

Sanjeev Sabnis, Mayank Jain, Kartik Verma

Pages: 36 - 46

This research article is related to a multi-state stress-strength model proposed by Eryilmaz and İşçioğlu (2011). It deals with (i) demonstration of the use of EM algorithm for the estimation of parameters of distributions of random variables representing strength and two stress levels. The numerical...

**Research Article**

## Prediction for Progressively Type-II Censored Competing Risks Data from the Half-Logistic Distribution

Essam K. AL-Hussaini, Alaa H. Abdel-Hamid, Atef F. Hashem

Pages: 36 - 48

Point and interval predictions of the s-th order statistic in a future sample are discussed. The informative sample is assumed to be drawn from a general class of distributions which includes, among others, Weibull, compound Weibull, Pareto, Gompertz and half-logistic distributions. The informative and...

**Research Article**

## On Characterization of Gompertz Distribution by Properties of Generalized Record Values

S. Minimol, P. Yageen Thomas

Pages: 38 - 45

In this chapter, we derive some recurrence relations satisfied by single and product moments of generalized record values arising from Gompertz and inverted Gompertz distributions. Further, we have obtained characterization of Gompertz and inverted Gompertz distributions based on certain properties of...

**Research Article**

## On Some New Results of Poverty Orderings and Their Applications

Mervat Mahdy

Pages: 38 - 52

The paper proposes to derive some new poverty indices which depend on aging classes. We also give some properties of it and show the connection between economic measure and new poverty measures these based on the concept of reversed residual incomes. In addition, the characterization of Pareto distribution...

**Research Article**

## A New Lifetime Model: The Gamma Extended Fréchet Distribution

Ronaldo V. da Silva, Thiago A.N. de Andrade, Diego B.M. Maciel, Renilma P. S. Campos, Gauss M. Cordeiro

Pages: 39 - 54

For the first time, a four-parameter lifetime model, called the gamma extended Fr´echet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, R´enyi entropy and reliability...

**Research Article**

## A New Method for Generating Discrete Analogues of Continuous Distributions

M. Ganji, F. Gharari

Pages: 39 - 58

In this paper we use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definition of delta and nabla discrete gamma distributions. The main result of this paper is unification of the continuous and discrete gamma distributions,...

**Research Article**

## Generalized Estimator of Finite population Variance

A.K.P.C. Swain

Pages: 45 - 51

In this paper a generalized class of finite population variance is suggested and its large sample bias and mean square error are derived. Further some special cases of this class are considered along with a numerical example to compute and compare their biases and mean square errors.

**Research Article**

## Estimation of a Matrix of Heterogeneity Parameters in Multivariate Meta-Analysis of Random-Effects Models

Abera Wouhib

Pages: 46 - 64

Multivariate meta-analysis has potential over its univariate counterpart. The most common challenge in univariate or multivariate meta-analysis is estimating heterogeneity parameters in non-negative domains under the random-effects model assumption. In this context, two new multivariate estimation methods...

**Research Article**

## On Partially Linear Single-Index Models with Missing Response and Error-in-Variable Predictors

Tsung-Lin Cheng, Yin-Ying Lin, Xuewen Lu, Radhey Singh

Pages: 46 - 64

In this paper, we consider a partially linear single-index model when missing responses and nonlinear regressors with measurement error are taken into account. Utilizing data imputation for missing values and regression calibration for error-prone regressors, we not only estimate the parameters in the...

**Research Article**

## Construction of Strata for a Model-Based Allocation Under a Superpopulation Model

Bhuwaneshwar Kumar Gupt, Md. Irphan Ahamed

Pages: 46 - 60

This paper considers the problem of optimum stratification for a model-based allocation under a superpopulation model. The equations giving optimum points of stratification have been derived and a few methods for finding approximately optimum points of stratification have been obtained from the equations....

**Research Article**

## Pathway Extension of Weibull-Gamma Model

T. Princy

Pages: 47 - 60

In this paper we develop a new family of Weibull-gamma model which is obtained by compounding a q-Weibull density with a two parameter gamma density. This class can be considered as a natural extension of the Weibull gamma model which accommodates various other useful statistical models. Properties of...

**Research Article**

## Finite Mixture Modeling via Skew-Laplace Birnbaum–Saunders Distribution

Mehrdad Naderi, Mahdieh Mozafari, Kheirolah Okhli

Pages: 49 - 58

Finite mixture model is a widely acknowledged model-based clustering method for analyzing data. In this paper, a new finite mixture model via an extension of Birnbaum–Saunders distribution is introduced. The new mixture model provide a useful generalization of the heavy-tailed lifetime model since the...

**Research Article**

## Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors

Mosisa Aga

Pages: 52 - 59

The purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametric...

**Research Article**

## Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors

S.K. Ghoreishi

Pages: 53 - 64

From practical point of view, in a two-level hierarchical model, the variance of second-level usually has a tendency to change through sub-populations. The existence of this kind of local (or intrinsic ) heteroscedasticity is a major concern in the application of statistical modeling. The main purpose...

**Research Article**

## A Symmetric Component Alpha Normal Slash Distribution: Properties and Inferences

Wenhao Gui, Pei-Hua Chen, Haiyan Wu

Pages: 55 - 66

In this paper, we introduce a new class of symmetric bimodal distribution. We define the distribution by means of a stochastic representation as the mixture of a symmetric component alpha normal random variable with respect to the power of a uniform random variable. The proposed distribution is more...

**Research Article**

## The Kumaraswamy Marshall-Olkin Log-Logistic Distribution with Application

Selen Cakmakyapan, Gamze Ozel, Yehia Mousa Hussein El Gebaly, G. G. Hamedani

Pages: 59 - 76

In this paper, we define and study a new lifetime model called the Kumaraswamy Marshall-Olkin log-logistic distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. The new model contains some well-known distributions as special cases such...

**Research Article**

## The Hjorth's IDB Generator of Distributions: Properties, Characterizations, Regression Modeling and Applications

Mustafa Ç. Korkmaz, Emrah Altun, Haitham M. Yousof, G. G. Hamedani

Pages: 59 - 74

We introduce a new flexible class of continuous distributions via the Hjorth's IDB model. We provide some mathematical properties of the new family. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. The maximum likelihood...

**Research Article**

## The beta exponentiated Lindley distribution

J.A. Rodrigues, A.P.C.M. Silva, G.G. Hamedani

Pages: 60 - 75

In this work, we study the beta exponentiated Lindley distribution which includes as special cases several models such as the Lindley, exponentiated Lindley and beta Lindley distributions. Some structural properties of the proposed distribution are studied including expressions for the moments. The estimation...

**Research Article**

## The Gumbel-Lomax Distribution: Properties and Applications

M.H. Tahir, M. Adnan Hussain, Gauss M. Cordeiro, G.G. Hamedani, M. Mansoor, M. Zubair

Pages: 61 - 79

We introduce a new four-parameter model called the Gumbel-Lomax distribution arising from the Gumbel- X generator recently proposed by Al-Aqtash (2013). Its density function can be right-skewed and reversed-J shaped, and can have decreasing and upside-down bathtub shaped hazard rate. Various structural...

**Research Article**

## On Inference of Overlapping Coefficients in Two Inverse Lomax Populations

Hamza Dhaker, El Hadji Deme, Salah El-Adlouni

Pages: 61 - 75

Overlapping coefficient is a direct measure of similarity between two distributions which is recently becoming very useful. This paper investigates estimation for some well-known measures of overlap, namely Matusita's measure ρ, Weitzman's measure Δ and Λ based on Kullback–Leibler. Two estimation...

**Research Article**

## McDonald log-logistic distribution with an application to breast cancer data

M.H. Tahir, Muhammad Mansoor, Muhammad Zubair, G.G. Hamedani

Pages: 65 - 82

We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the...

**Research Article**

## Transmuted Generalized Gompertz distribution with application

Muhammad Shuaib Khan, Irene Lena Hudson, Robert King

Pages: 65 - 80

This paper introduces the four parameter transmuted generalized Gompertz distribution which includes the transmuted Gompertz, transmuted generalized exponential, transmuted exponential, Gompertz, generalized exponential and exponential distributions as special cases and studies its statistical properties....

**Research Article**

## Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Mohd Arshad, Qazi Azhad Jamal

Pages: 65 - 78

In this paper, we consider a general family of distributions generated by Topp–Leone distribution (known as TL family of distributions) proposed by Rezaei et al. [1]. We consider the problem of estimation of the shape parameter, scale parameter, and reliability function based on record data from TL family...

**Research Article**

## Prediction Intervals for k-records in Terms of Current Records

M. Chahkandi, J. Ahmadi

Pages: 67 - 82

In this paper, we discuss the prediction of k-records from the future sequence based on observed current records of either kind upper or lower, record coverage and k-records from the same distribution. It is shown that the coverage probability of all proposed prediction intervals are distribution-free....

**Research Article**

## Construction, Characterization, Estimation and Performance Analysis of Selection Generalized Nakagami Distributions with Environmental Applications

Mervat Mahdy, Dina Samir

Pages: 75 - 90

In this article, a selection of Nakagami distribution is investigated. Some properties of the model with some plots of the density function are illustrated. Additionally, weighted of the one-sided Gaussian distribution, Generalized Rayleigh distribution are discussed as a special case of Generalized...

**Research Article**

## Stochastic Properties of the Weighted Hazard Rate Order

S. Izadkhah, M. Amini, G.R. Mohtashami Borzadaran

Pages: 76 - 88

The hazard rate order between two weighted distributions with a given weight function is considered as a new stochastic order called weighted hazard rate order. The influences of biased sampling methods on properties of the hazard rate order are usefully pointed out with this weighted order. We first...

**Research Article**

## Generalized Skew Laplace Random Fields: Bayesian Spatial Prediction for Skew and Heavy Tailed Data

Mohammad Mehdi Saber, Alireza Nematollahi, Mohsen Mohammadzadeh

Pages: 76 - 85

Earlier works on spatial prediction issue often assume that the spatial data are realization of Gaussian random field. However, this assumption is not applicable to the skewed and kurtosis distributed data. The closed skew normal distribution has been used in these circumstances. As another alternative,...

**Research Article**

## Odd Generalized Exponential Flexible Weibull Extension Distribution

Abdelfattah Mustafa, Beih S. El-Desouky, Shamsan AL-Garash

Pages: 77 - 90

In this article we introduce a new four - parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and mode,...

**Research Article**

## Bayes and Non-Bayes Estimation of Change Point in Nonstandard Mixture Inverse Weibull Distribution

Masoud Ganji, Roghayeh Mostafayi

Pages: 79 - 86

We consider a sequence of independent random variables X1,X2,…,Xm,…,Xnn≥3 exhibiting a change in the probability distribution of the data generating mechanism. We suppose that the distribution changes at some point, called a change point, to a second distribution for the remaining observations. We propose...

**Research Article**

## Multi-stage Optional Unrelated Question RRT Model

Anu Chhabra, B.K. Dass, Samridhi Mehta

Pages: 80 - 95

Sihm et al. (2014) introduced modified optional unrelated question RRT model in both binary and quantitative response situations wherein the prevalence of the sensitive variable and the sensitivity level of the underlying sensitive question could be estimated simultaneously without using a split sample...

**Research Article**

## A study of methods for estimating in the exponentiated Gumbel distribution

K. Fathi, S.F. Bagheri, M. Alizadeh, M. Alizadeh

Pages: 81 - 95

The exponentiated Gumbel model has been shown to be useful in climate modeling including global warming problem, flood frequency analysis, offshore modeling, rainfall modeling and wind speed modeling. Here, we consider estimation of the PDF and the CDF of the exponentiated Gumbel distribution. The following...

**Short Communication**

## A characterization of the normal distribution

Hans Volkmer

Pages: 83 - 85

It is shown that the normal distribution with mean zero is characterized by the property that the product of its characteristic function and moment generating function is equal to 1.

**Research Article**

## On Some Predictive Ratio Type Estimators in Two Stage Sampling

A.K.P.C. Swain, Sitanshu Shekhar Mishra, B.K. Pradhan

Pages: 83 - 91

Some predictive ratio type estimators in two stage sampling are derived following the model free predictive criterion proposed by Basu (1971) and these estimators are compared with the classical multistage ratio estimator and also with Smith’s (1969) multistage ratio estimator. A numerical illustration...

**Research Article**

## Some new results for the Kumaraswamy modified Weibull distribution

Gauss M. Cordeiro, Antonio C.R. Braga Junior, Clarice G.B. Demétrio, Edwin M.M. Ortega, Rodrigo R. Pescim

Pages: 86 - 104

We study some mathematical properties of the Kumaraswamy modified Weibull distribution pioneered by Cordeiro et al. [4] not discussed by these authors. This model is quite flexible for analyzing positive data since it contains as special models some widely-known distributions, such as the KumaraswamyWeibull,...

**Research Article**

## Transmuted Lower Record Type Fréchet Distribution with Lifetime Regression Analysis Based on Type I-Censored Data

Caner Tanış, Buğra Saraçoğlu, Coşkun Kuş, Ahmet Pekgör, Kadir Karakaya

Pages: 86 - 96

This paper introduces a new lifetime distribution by mixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussed with five estimators. A Monte Carlo simulation study is carried out to evaluate the risk behavior...

**Research Article**

## A New Generalized Two-Sided Class of the Distributions Via New Transmuted Two-Sided Bounded Distribution

O. Kharazmi, M. Zargar

Pages: 87 - 102

In the present paper, we first consider a generalization of the standard two-sided power distribution so-called the transmuted two-sided distribution, and then extend proposed idea to generalized two-sided class of distributions, introduced by Korkmaz and Genç [1]. Some statistical and reliability properties...

**Research Article**

## On the Properties of Estimates of Monotonic Mean Vectors for Multivariate Normal Distributions

Abouzar Bazyari

Pages: 89 - 106

.Problems concerning estimation of parameters and determination the statistic, when it is known a priori that some of these parameters are subject to certain order restrictions, are of considerable interest. In the present paper, we consider the estimators of the monotonic mean vectors for two dimensional...

**Research Article**

## Combined Intra- and Inter- Block Analysis of Balanced Ternary Designs

Sobita Sapam, B. K. Sinha, N.K. Mandal

Pages: 91 - 100

In the present paper an attempt has been made to study the inter–and intra-block estimation of treatment effects contrasts with random block effects in the context of balanced ternary designs. The analysis is illustrated through examples.

**Research Article**

## Fuzzy C-Means Clustering Using Asymmetric Loss Function

Israa Abdzaid Atiyah, Adel Mohammadpour, Narges Ahmadzadehgoli, S. Mahmoud Taheri

Pages: 91 - 101

In this work, a fuzzy clustering algorithm is proposed based on the asymmetric loss function instead of the usual symmetric dissimilarities. Linear Exponential (LINEX) loss function is a commonly used asymmetric loss function, which is considered in this paper. We prove that the negative likelihood of...

**Research Article**

## Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data Generation

Elsayed A.H. Elamir

Pages: 92 - 105

Multiplicative-binomial distribution is one of the distributions that allows for over-dispersion and under-dispersion relative to the standard binomial distribution. It will be shown that the multiplicative-binomial distribution can be a very useful model for these situations. Moreover, the confidence...

**Research Article**

## On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data

Fanny Leroy, Jean-Yves Dauxois, Pascale Tubert-Bitter

Pages: 96 - 107

We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent nonidentically...

**Research Article**

## Optimal Structure (k) Designs for Comparing Test Treatments with a Control

M.A. Chowdhury, S. Mandal, D.K. Ghosh, S.C. Bagui

Pages: 96 - 107

Mukerjee (1979) introduced structure (k) property of a factorial design. In this article, we introduce structure (k1), structure (k2) and structure (k1k2) properties of a factorial design. We establish properties of each of these structure designs in terms of the incidence and characteristic matrices...

**Research Article**

## On Seemingly Unrelated Regression Model with Skew Error

Omid Akhgari, Mousa Golalizadeh

Pages: 97 - 110

Sometimes, invoking a single causal relationship to explain dependency between variables might not be appropriate particularly in some economic problems. Instead, two jointly related equations, where one of the explanatory variables is endogenous, can represent the actual inheritance inter-relationship...

**Research Article**

## On Some Aspects of a New Class of Two-Piece Asymmetric Normal Distribution

C. Satheesh Kumar, M.R. Anusree

Pages: 101 - 121

Through this chapter, we introduce a new class of two-piece asymmetric normal distribution suitable for asymmetric and plurimodal situations. We study some important aspects of this distribution by deriving explicit expressions for its distribution function, characteristic function, reliability measures...

**Research Article**

## A New Flexible Discrete Distribution with Applications to Count Data

Anwar Hassan, Gulzar Ahmad Shalbaf, Sheikh Bilal, Adil Rashid

Pages: 102 - 108

In this paper we have explored a new discrete probability mass function that has been generated through compounding mechanism. This newly proposed probability mass function is essentially a mixture of Poisson and Ailamujia distribution. Furthermore the parameter estimation has also been discussed by...

**Research Article**

## Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

Shahjahan Khan, Budi Pratikno, Shafiqur Rahman, M. Zakir Hossain

Pages: 103 - 112

The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This...

**Research Article**

## Beta Burr XII OR Five Parameter Beta Lomax Distribution: Remarks and Characterizations

Z. Javanshiri, M. Maadooliat

Pages: 105 - 110

The distributions taken up in two recently published papers are compared and certain characterizations of them are presented. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the nth order statistic; (iii) truncated...

**Research Article**

## New classes at Specific Age: Properties and Testing hypotheses

M.A.W. Mahmoud, M.E. Moshref, A.M. Gadallah, A.I. Shawky

Pages: 106 - 119

In this article we introduce new classes of life distributions namely new better (worse) than used in expectation at specific age t0 NBUE-t0 (NWUE-t0) and harmonic new better (worse) than used in expectation at specific age t0 HNBUE-t0 (HNWUE-t0). The closure properties under various reliability operations...

**Research Article**

## Bayesian Estimation Based on Progressively Type-II Censored Samples from Compound Rayleigh Distribution

Rashad Mohamed EL-Sagheer, Mohamed Ahsanullah

Pages: 107 - 122

This paper considers inference under progressive type-II censoring scheme with a compound Rayleigh failure time distribution. The maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the compound Rayleigh distribution (CRD) distribution are derived. A Bayesian approach using...

**Research Article**

## Characterizing Distributions by Linearity of Regression of Generalized Order Statistics

Abbas Rasouli, S. Samadi, Mohammad Ahsanullah

Pages: 108 - 114

Let X1,..., Xn be a random sample from an absolutely continuous (with respect to Lebesgue measure) distribution with the corresponding generalized order statistics X(1, n, m~, k),..., X(n, n, m~, k). In this paper, we present some characterization of distributions when linearity of regression E[X(s,...

**Research Article**

## Likelihood Inference in A Multivariate Spatial GLMM with Skew Gaussian Random Effects Using the Slice-SAB Algorithm

Firoozeh Rivaz, Majid Jafari Khaledi

Pages: 108 - 116

This paper introduces a multivariate skew Gaussian process and uses it to extend the family of multivariate spatial generalized linear mixed models to include skew Gaussian random effects. In this setting, the param- eter estimation encounters problems because the likelihood function involves high dimensional...

**Research Article**

## Sample Design and Estimation of Parameters of Half Logistic Distribution Using Generalized Ranked-Set Sampling

A. Adatia, A.K.MD. Ehsanes Saleh

Pages: 109 - 117

The ranked-set sampling technique has been generalized so that a more efficient estimator may be obtained. This technique allows more than one unit from each set to be quantified. Consequently, the number of units to be sampled may be reduced significantly and as a result, the corresponding cost would...

**Research Article**

## Testing Exponentiality Against UBAC Using Kernel Methods

M.M. Mohie El-Din, S.E. Abu-Youssef, M.KH. Hassan

Pages: 111 - 121

In this paper, the problem of testing exponentiality against used better than aged in convex ordering classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's...

**Research Article**

## A Note on Generalization of the Simplest Time-Dependent Discrete Markov Process: Linear Growth Process With Immigration-Emigration

Bijoy Kumar Pradhan, Priyaranjan Dash, Upasana

Pages: 111 - 131

Lineargrowth process with immigration and emigration is the general model in the study of population in biological and ecological systems, and their transient analysis is the most important factor in the understanding of the structural behavior of such systems. The probability-generating function π(z,...

**Research Article**

## Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes III

Amadou Diadié Bâ, Gane Samb Lo, Diam Bâ

Pages: 113 - 122

In the two previous papers of this series, the main results on the asymptotic behaviors of empirical divergence measures based on wavelets theory have been established and particularized for important families of divergence measures like Rényi and Tsallis families and for the Kullback-Leibler measures....

**Research Article**

## Moments of Record Values and Characterizations of Marshall-Olkin Extended Distribution

G.G. Hamedani, Miroslav M. Ristić

Pages: 115 - 124

Moments of the mth upper record value XU(m), m≥1, and the joint moments of the mth and nth upper record values XU(m) and XU(n), n>m≥1, of a random variable X with Marshall-Olkin Extended distribution are presented. Certain characterizations of this distribution based on hazard function and a simple...

**Research Article**

## Bayesian Analysis of a 3-Component Mixture of Rayleigh Distributions under Type-I Right Censoring Scheme

Muhammad Tahir, Muhammad Aslam, Zawar Hussain

Pages: 117 - 136

Since the last few decades, constructing flexible parametric classes of probability distributions has been the most popular approach in the Bayesian analysis. As compared to simple probability models, a mixture model of some suitable lifetime distributions may be more capable of capturing the heterogeneity...

**Research Article**

## Robust Mixture Regression Based on the Mixture of Slash Distributions

Hadi Saboori, Ghobad Barmalzan, Mahdi Doostparast

Pages: 118 - 132

The traditional estimation of Mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers and heavy-tailed errors. In this paper, we propose a robust Mixture regression models in which a mixture of slash distributions is assumed for the errors. Using...

**Research Article**

## On Discrete Residual and Past Measures of Inaccuracy

Vikas Kumar, Richa Thapliyal, H.C. Taneja

Pages: 120 - 128

The present communication considers a discrete dynamic measure of inaccuracy between two residual and past lifetime distributions. Under the assumption that the true distribution F and reference distribution G satisfy the proportional hazard model (PHM) and proportional reversed hazard model (PRHM),...

**Research Article**

## The Kumaraswamy-Half-Cauchy distribution: properties and applications

Indranil Ghosh

Pages: 122 - 134

In this article, based on the half-Cauchy distribution, we propose a new distribution called Kumaraswamy- Half-Cauchy distribution. Various explicit expressions for it’s moments, generating and quantile functions, mean deviations, reliability parameter, density function of the order statistics and their...

**Research Article**

## Recurrence Relations for Single and Product Moments of Dual Generalized Order Statistics from a General Class of Distributions

Jagdish Saran, Narinder Pushkarna, Rashmi Tiwari

Pages: 123 - 130

In this paper we derive some general recurrence relations between single and product moments of dual gener- alized order statistics from a general class of distributions, thus generalizing and unifying the earlier results in this direction due to several authors.

**Research Article**

## Estimating the parameters of Lomax distribution from imprecise information

Abbas Pak, Mohammad Reza Mahmoudi

Pages: 122 - 135

Traditional statistical approaches for estimating the parameters of Lomax distribution have dealt with precise information. However, in real world situations, some information about an underlying system might be imprecise and are represented in the form of fuzzy information. In this paper, we consider...

**Research Article**

## Some Characterization Results Based on the Mean Vitality Function of the First-Order Statistics

A. Toomaj, A. Shirvani

Pages: 123 - 128

In this paper, we investigate some new properties of the mean vitality function (MVF) of a random variable, proposed by A. Toomaj, M. Doostparast, J. Stat. Theory Appl. 13 (2013), 189–195. Specifically, we explore properties of MVF and study under what conditions the MVF of the first-order statistics...

**Research Article**

## The Additive Weibull-Geometric Distribution: Theory and Applications

I. Elbatal, M.M. Mansour, Mohammad Ahsanullah

Pages: 125 - 141

In this paper, we introduce a new class of lifetime distributions which is called the additive Weibull geometric (AWG) distribution. This distribution obtained by compounding the additive Weibull and geometric distributions. The new distribution has a number of well-known lifetime special sub-models...

**Research Article**

## The Kumaraswamy Pareto distribution

Marcelo Bourguignon, Rodrigo B. Silva, Luz M. Zea, Gauss M. Cordeiro

Pages: 129 - 144

The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution, is introduced and studied. The new distribution can have a decreasing and upside-down bathtub failure...

**Research Article**

## Generalized Order Statistics from Marshall–Olkin Extended Exponential Distribution

Haseeb Athar, Nayabuddin, Saima Zarrin

Pages: 129 - 135

A.W. Marshall, I. Olkin, Biometrika. 84 (1997), 641–652, introduced an interesting method of adding a new parameter to an existing distribution. The resulting new distribution is called as Marshall–Olkin extended distribution. In this paper some recurrence relations for marginal and joint moment generating...

**Research Article**

## On Some Nonparametric Tests For Partially Observed Correlated Data: Proposing New Tests

Hani M. Samawi, Lili Yu, Robert Vogel

Pages: 131 - 155

Correlated or matched data is frequently collected under many study designs in applied sciences such as the social, behavioral, economic, biological, medical, epidemiologic, health, public health, and drug developmental sciences in order to have more efficient design and to control for potential confounding...

**Research Article**

## Generalized Rank Mapped Transmuted Distribution for Generating Families of Continuous Distributions

M. A. Ali, Haseeb Athar

Pages: 132 - 148

This study introduces generalized transmuted family of distributions. We investigate the special cases of our generalized transmuted distribution to match with some other generalization available in literature. The transmuted distributions are applied to Weibull distribution to find generalized rank...

**Research Article**

## Modeling Vehicle Insurance Loss Data Using a New Member of T-*X* Family of Distributions

Zubair Ahmad, Eisa Mahmoudi, Sanku Dey, Saima K. Khosa

Pages: 133 - 147

In actuarial literature, we come across a diverse range of probability distributions for fitting insurance loss data. Popular distributions are lognormal, log-t, various versions of Pareto, log-logistic, Weibull, gamma and its variants and a generalized beta of the second kind, among others. In this...

**Research Article**

## On Moment Generating Function of Generalized Order Statistics From Extended Type II Generalized Logistic Distribution

Devendra Kumar

Pages: 135 - 150

In this paper, explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from extended type II loglogistic distribution. Further the results are deduced for moments of k -- th record values and ordinary order statistics.