Abstract

This article presents method of constructing tests for the hypothesis on shape parameter 𝛽 of the family of lifetime distributions under progressive censoring. We derive three test statistics 𝑄_(𝑠𝑑), F and 𝑄₁. The performance of these statistics, in terms of power, is studied through simulation for different values of shape parameter of Gompertz distribution, Burr-XII distribution, bathtub distribution, and Weibull distribution. For these distributions, it is concluded that either a test 𝑄_(𝑠𝑑), or test 𝑄₁ performs better than test F in case of large samples whereas test F performs better than other tests 𝑄_(𝑠𝑑)and 𝑄₁ in case of small samples when the shape parameter is not equal to the value under null hypothesis.

Author: Ashok Shanubhogue and Rajendra G. Desai

Received on: November, 2018

Accepted on: October, 2019