We consider the problem of providing the exact distribution of the likelihood ratio test (LRT) statistic for testing the homogeneity of scale parameters of $$ k \ge 2 $$
 two-parameter exponential distributions. To this end, we apply the Millen inverse transform and the Jacobi polynomial expansion to the moments of LRT statistic. We consider the problem when the data are either complete or censored under the different kinds of Type II censoring, such as the Type II right, progressively Type II right, and double Type II censoring schemes. We also discuss the exact null distribution of the LRT when the data are censored under the Type I censoring scheme.

On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples

This paper considers estimation of the stress–strength reliability when the stress and strength follow two-parameter exponential distributions having different location parameters and a com...

Inference on stress–strength reliability for exponential distributions with a common scale parameter

In this paper, we present eleven approaches for testing the equality of scale parameters in gamma distributions when shape parameters are known. These approaches are applicable to other problems such as testing homogeneity of variances in normal distributions, verifying equality of scale-like parameters in inverse Gaussian distributions, and comparing scale parameters in two-parameter exponential distributions with censored data or K-record values. The performance of the proposed tests is compared in terms of empirical size and power using Monte Carlo simulation. Finally, the proposed methods are illustrated using two real data examples.

Comparing scale parameters in several gamma distributions with known shapes

The modified Tiku test and the modified likelihood ratio test proposed by Tiku and Vaughan (1991) for k=2 exponential populations are extended to . k > 2 populations. These tests are shown to be more powerful than the test proposed by Kambo and Awad (1985). Unlike the Kambo-Awad test, the proposed tests are shown to have almost symmetric power functions. Further, these tests can be applied when there is both left or right censoring present, in contrast to the tests of Sukhatme (1937), Bain and Englehardt (1991) and Elewa et al. (1992), who assume that there is no left censoring.

Testing the equality of location parameters of exponential populations from censored samples

In this paper, null distribution of the likelihood ratio criterion for testing the quality of scale parameters of p(p>2) two parameter exponential distributions for the case of equal sample sizes is obtained in a closed form for the first time. A short table of the critical values of the test statistic is also presented.

On a test of equality of scale parameters of several exponential distributions

In this paper, the distribution of the likelihood ratio criterion for testing the equality of several two–parameter exponential distributions based on type II cen-sored samples is obtained in a computational form. This is then used to compute the significance points of the likelihood ratio test statistic.

B. N. Nagarsenker

Papers

On a test of equality of scale parameters of several exponential distributions

On a test of equality of exponential populations based on censored samples