Abstract
In this paper, we introduce some new goodness-of-fit tests for the Rayleigh distribution based on Jeffreys, Lin-Wong and Renyi divergence measures. Then, the new proposed tests are compared with other tests in the literature. We compare the power of considered tests for some alternative distributions whose powers are calculated by Monte Carlo simulation. Finally, we conclude that entropy-based tests have a good performance in terms of power and among them Jeffreys test is the best one.
Highlights
Identifying true distribution of real data is an important part of reliability, life testing and survival analysis
We propose some new GOF tests for the Rayleigh distribution which are based on some divergence measures
We propose using some popular divergence measures such as Jeffreys, Lin-Wong and Rényi divergence for checking the Rayleigh distribution and we guess using these divergence measures leads to a better performance in terms of power against other proposed tests in the statistical literature
Summary
Identifying true distribution of real data is an important part of reliability, life testing and survival analysis. The Rayleigh distribution was originally offered by a physicist, Lord Rayleigh (1880), in connection with an acoustics problem. It has been used to model data that are skewed to the right; such as life data which arises in many areas of applications. Siddiqui (1962) discussed the origin and properties of the Rayleigh distribution. One major application of this model is used in analyzing wind speed data. The origin and other aspects of this distribution can be found in Siddiqui (1962), Miller and Sackrowttz (1967). For more details on the Rayleigh distribution the reader is referred to Johnson et al (1994)
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