Goodness-of-fit tests for the Compound Rayleigh distribution with application to real data

Abstract

An important problem in statistics is to obtain information about the form of the population from which the sample is drawn. Goodness of fit (GOF) tests is employed to determine how well the observed sample data “fits” some proposed model. The well known standard goodness of fit tests; Kolomogorov-Smirnov (KS), Cramer von Mises (CVM) and Anderson-(AD) tests are used for continuous distributions. When the parameters are unknown, the standard tables for these tests are not valid. The complete sample procedures of goodness of fit tests are inappropriate for use with censored samples. The critical values obtained from published tables of the complete sample test statistic are necessarily conservative. In this paper, we obtain the tables of critical values of modified Kolmogorov-Smirnov (KS) test, Cramer-Von Mises (CVM) test and Anderson-Darling (AD) test for the Compound Rayleigh (CR) distribution with unknown parameters in the case of complete and type II censored samples. Furthermore, we present power comparison between KS test, CVM test and AD test for a number of alternative distributions. Applications of the considered distribution to real medical data sets given by Stablein et al. (1981) are presented.

A Study on Alpha Power Lomax Distribution

“…Data II: (Natural phenomena) Badr (2019) presented the consist of 30 successive March precipitation (in inches) observations. 77, 52, 90, 174, 162, 205, 81, 131, 120, 32, 195, 95, 120, 81, 47,281, 143, 187, 337, 118, 220, 135, 300, 475, 309, 248, 151, 96, 210,189. Table 7 displays descriptive statistics for this data.…”

Goodness-of-fit tests for the beta Gompertz distribution

“…The first, second and third data sets were presented in Abu-Zinadah and Hajar [12,13]. Moreover, the fourth and sixth data sets have been taken from Badr [17], the fifth data set from Best et al [21], the rest of the data sets from Shanker et al [22] and the tenth data from Cakmakyapan and Ozal [23].…”

“…Later on, Lenart and Missov [16] introduced the goodness of fit for the Gompertz distribution with four measures and presented the critical values by an empirical distribution of the test statistics. Furthermore, Badr [17] studied the goodness of fit tests for the compound Rayleigh distribution with application real data for complete and type II censored samples.…”

Modified Goodness of Fit Tests for Rayleigh Distribution

“…Among the many authors that haves constructed the tables of critical values for various modified goodness of fit tests for different types of distribution. Further details can be seen in [1,3,9,10,11].…”

“…3 show critical values for modified KS, CvM and AD tests.Based on Table1-3, critical values of modified KS, CvM and AD test increase as the significant level (  ) decrease.For modified CvM and AD tests, the critical values increase as the sample size increases while the critical values for modified KS decrease as sample size increases. Moreover, for the specific sample size the critical values for modified AD test is the biggest for all significant levels.…”