On testing More IFRA Ordering-II

TL;DR

This paper introduces a new statistical test for comparing life distributions based on the IFRA ordering, utilizing U-statistics, with proven asymptotic properties and practical application to reliability data.

Contribution

A novel U-statistics based test for IFRA ordering that handles known and unknown baseline distributions, with asymptotic analysis and real data application.

Findings

The test has well-defined asymptotic distribution.

It performs favorably compared to existing tests.

Successfully applied to real reliability data.

Abstract

Suppose F and G are two life distribution functions. It is said that F is more IFRA than G (written by F<_* G) if G^(-1) F(x) is starshaped on (0,infty). In this paper, the problem of testing H_0:F=_* G against H_1:F<_* G and F \neq_* G is considered in both cases when G is known and when G is unknown. We propose a new test based on U-statistics and obtain the asymptotic distribution of the test statistics. The new test is compared with some well known tests in the literature. In addition, we apply our test to a real data set in the context of reliability.