Journal of Statistical Theory and Applications

Volume 18, Issue 1, March 2019, Pages 65 - 78

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

Authors
Mohd Arshad*, Qazi Azhad Jamal
Department of Statistics and Operations Research, Aligarh Muslim Univeristy, Aligarh, Uttar Pradesh, India
*Correspondence author. Email: arshad.iitk@gmail.com
Corresponding Author
Mohd Arshad
Received 13 November 2017, Accepted 6 August 2018, Available Online 22 April 2019.
DOI
10.2991/jsta.d.190306.008How to use a DOI?
Keywords
Topp–Leone-generated family of distributions; ML estimators; Bayesian inference; symmetric loss function; asymmetric loss function; Bayes estimators; reliability function
Abstract

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 of distributions. We derive the maximum likelihood estimator (MLE) for shape parameter, scale parameter, and reliability function. We have also obtained UMVUE (uniformly minimum-variance unbiased estimator) for reliability function when scale parameter is known. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Further, we have predicted future record values using Bayesian approach. A numerical comparison of various estimators is also reported.

Copyright
© 2019 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
18 - 1
Pages
65 - 78
Publication Date
2019/04/22
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.d.190306.008How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Mohd Arshad
AU  - Qazi Azhad Jamal
PY  - 2019
DA  - 2019/04/22
TI  - Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records
JO  - Journal of Statistical Theory and Applications
SP  - 65
EP  - 78
VL  - 18
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.190306.008
DO  - 10.2991/jsta.d.190306.008
ID  - Arshad2019
ER  -