Goodness of fit tests for Rayleigh distribution

TL;DR

This paper introduces new goodness of fit tests for Rayleigh distribution applicable to complete and censored data, utilizing U-Statistics and empirical likelihood, with validation through simulations and real data examples.

Contribution

It presents novel goodness of fit tests for Rayleigh distribution that handle both complete and censored data using U-Statistics and jackknife empirical likelihood methods.

Findings

The tests have good asymptotic properties.

Simulation studies confirm the effectiveness of the tests.

Real data applications demonstrate practical utility.

Abstract

We develop a new goodness fit test for Rayleigh distribution for complete as well as right censored data. We use U-Statistic theory to derive the test statistic. First we develop a test for complete data and then discuss, how right censored observations can be incorporated in the testing procedure. The asymptotic properties of the test statistics in both uncensored and censored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We illustrate the procedures using real data sets. We also provide, a goodness of fit test for standard Rayleigh distribution based on jackknife empirical likelihood.