Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution

Bahman Tarvirdizade; Hossein Kazemzadeh Gharehchobogh Hossein Kazemzadeh Gharehchobogh

EN

Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution

Abstract

Our interest is in estimating the stress-strength reliability Pr(X > Y ) based on lower record values when X and Y are two independent but not identically distributed Burr type X random variables. The maximum likelihood estimator, Bayes and empirical Bayes estimators using Lindleys approximations, are obtained and their properties are studied. The exact confidence interval, as well as the Bayesian credible sets are obtained. Two examples are presented in order to illustrate the inferences discussed in the previous sections. A Monte Carlo simulation study is conducted to investigate and compare the performance of different types of estimators presented in this paper and to compare them with some bootstrap intervals.

Keywords

Likelihood estimation,Bayesian estimation,Burr type X distribution,Record values,Stress-strength reliability,Lindley approximation

References

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Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

Bahman Tarvirdizade ^*

Hossein Kazemzadeh Gharehchobogh Hossein Kazemzadeh Gharehchobogh This is me

Publication Date

February 1, 2016

Submission Date

October 17, 2014

Acceptance Date

January 2, 2015

Published in Issue

Year 2016 Volume: 45 Number: 1

IZ

https://izlik.org/JA49ZT69BJ

Cite

RIS / Bibtex

APA

Tarvirdizade, B., & Hossein Kazemzadeh Gharehchobogh, H. K. G. (2016). Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution. Hacettepe Journal of Mathematics and Statistics, 45(1), 267-278. https://izlik.org/JA49ZT69BJ

AMA

1.Tarvirdizade B, Hossein Kazemzadeh Gharehchobogh HKG. Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution. Hacettepe Journal of Mathematics and Statistics. 2016;45(1):267-278. https://izlik.org/JA49ZT69BJ

Chicago

Tarvirdizade, Bahman, and Hossein Kazemzadeh Gharehchobogh Hossein Kazemzadeh Gharehchobogh. 2016. “Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution”. Hacettepe Journal of Mathematics and Statistics 45 (1): 267-78. https://izlik.org/JA49ZT69BJ.

EndNote

Tarvirdizade B, Hossein Kazemzadeh Gharehchobogh HKG (February 1, 2016) Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution. Hacettepe Journal of Mathematics and Statistics 45 1 267–278.

IEEE

[1]B. Tarvirdizade and H. K. G. Hossein Kazemzadeh Gharehchobogh, “Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 1, pp. 267–278, Feb. 2016, [Online]. Available: https://izlik.org/JA49ZT69BJ

ISNAD

Tarvirdizade, Bahman - Hossein Kazemzadeh Gharehchobogh, Hossein Kazemzadeh Gharehchobogh. “Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution”. Hacettepe Journal of Mathematics and Statistics 45/1 (February 1, 2016): 267-278. https://izlik.org/JA49ZT69BJ.

JAMA

1.Tarvirdizade B, Hossein Kazemzadeh Gharehchobogh HKG. Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution. Hacettepe Journal of Mathematics and Statistics. 2016;45:267–278.

MLA

Tarvirdizade, Bahman, and Hossein Kazemzadeh Gharehchobogh Hossein Kazemzadeh Gharehchobogh. “Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 1, Feb. 2016, pp. 267-78, https://izlik.org/JA49ZT69BJ.

Vancouver

1.Bahman Tarvirdizade, Hossein Kazemzadeh Gharehchobogh Hossein Kazemzadeh Gharehchobogh. Inference on Pr(X > Y) Based on Record Values from the Burr Type X Distribution. Hacettepe Journal of Mathematics and Statistics [Internet]. 2016 Feb. 1;45(1):267-78. Available from: https://izlik.org/JA49ZT69BJ