On Progressive Type-II Censored Samples from Alpha Power Exponential Distribution

Mukhtar M Salah,Hijaz Ahmad

doi:10.1155/2020/2584184

Abstract

In this paper the two-parameter α -power exponential distribution is studied. We study the two-parameter α -power exponential μ , λ distribution with the location parameter μ > 0 and scale parameter λ > 0 under progressive Type-II censored data with fixed shape parameter α . We estimate the maximum likelihood estimators of these unknown parameters numerically since it cannot be solved analytically. We use the approximate best linear unbiased estimators μ ∗ and λ ∗ , as an initial guesses to obtain the MLEs μ ^ and λ ^ . We estimate the interval estimation of these unknowns’ parameters. Monte Carlo simulations are performed and data examples have been provided for illustration and comparison.

Highlights

(2) Assume that an experiment is stopped at Rth failure the resulting data is defined as Type-II censored sample; note here Rth failure is considered to be fixed, while XR:n denotes a random experiment duration
(3) Progressive censoring sample: assume s identical items are placed on a life-testing experiment, and it is decided to observe only k failures, and censor the remaining s − k items progressively as follows
Mahdavi and Kundu [11] present a new method to add a new parameter to a family of distribution. ey named it as α- power transformation (APT) method. ey applied the APT method to a specific class of distribution such as the exponential distribution, and they called this new distribution as the two-parameter α-power exponential (APE) distribution

Summary

Introduction

(2) Assume that an experiment is stopped at Rth failure the resulting data is defined as Type-II censored sample; note here Rth failure is considered to be fixed, while XR:n denotes a random experiment duration. It is named as progressive Type-II censoring sample. Zk:k:s be a progressively Type-II censored sample and

Results

Conclusion