Estimation procedures for reliability functions of Kumaraswamy-G Distributions based on Type II Censoring and the sampling scheme of Bartholomew

Aditi Chaturvedi; Surinder Kumar

doi:10.21307/stattrans-2022-008

Estimation procedures for reliability functions of Kumaraswamy-G Distributions based on Type II Censoring and the sampling scheme of Bartholomew

Aditi Chaturvedi Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India , Surinder Kumar Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India Statistics in Transition new series, vol. 23, 2022, 1, pages: 129-152 Published online: 15 March 2022 DOI 10.21307/stattrans-2022-008 Citation: Chaturvedi A., Kumar S., (2022). Estimation procedures for reliability functions of Kumaraswamy-G Distributions based on Type II Censoring and the sampling scheme of Bartholomew, Statistics in Transition new series, 23(1), pp. 129–152. https://doi.org/10.21307/stattrans-2022-008

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ABSTRACT

In this paper, we consider Kumaraswamy-G distributions and derive a Uniformly Minimum Variance Unbiased Estimator (UMVUE) and a Maximum Likelihood Estimator (MLE) of the two measures of reliability, namely R(t) = P(X > t) and P = P(X > Y) under Type II censoring scheme and sampling scheme of Bartholomew (1963). We also develop interval estimates of the reliability measures. A comparative study of the different methods of point estimation has been conducted on the basis of simulation studies. An analysis of a real data set has been presented for illustration purposes.

KEYWORDS

interval estimation, Kumaraswamy-G distributions, Monte-Carlo simulation, point estimation.

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