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.
Highlights
Compound Rayleigh distribution is one of the models which are useful in different areas of statistics
We present power comparison between KS test, Cramer von Mises (CVM) test and AD test for a number of alternative distributions
The Monte Carlo procedure for the critical values determination described in the following steps: Step (1): Suppose that X is random variable follows Compound Rayleigh distribution, and for a fixed sample size, we generate the random sample X1, X2, ..., Xn from the CR distribution with parameters α and β
Summary
Compound Rayleigh distribution is one of the models which are useful in different areas of statistics. When F0(x) is completely specified (i.e. does not contain unknown parameters) and the data are uncensored the tests are all distribution free and percentage points for the various test statistics are generally known. The KS, CVM and AD test statistics are all distribution free and percentage points for these statistics are generally known when F0(x) is completely specified and the data are uncensored This is no longer the case when data are censored or F0(x) involves unknown parameters. Monte Carlo methods are often used to obtain critical values for the modified goodness of fit tests with estimated parameters.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call