Abstract
A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.
Highlights
The Rayleigh distribution is very popular among lifetime distributions
We considered Exponential, Rayleigh, Generalized Exponential (GE) (Gupta and Kundu, 2001), Generalized Rayleigh(GR)(Kundu and Raqab, 2005) distributions
We obtained critical values for Marshal-Olkin Extended Rayleigh distribution using Monte Carlo simulations for different sample sizes n and significance level γ
Summary
The Rayleigh distribution is very popular among lifetime distributions. Some of the areas where it is used are the study of vibrations and waves, theory of communication to explain instantaneous peak power and hourly median of signals received at a radio, to model wind speed under certain circumstances at wind turbine sites in a year and for modeling the lifetimes of devices. Distribution functions based goodness of fit tests give equal weight to discrepancy between theoretical distribution and empirical distribution functions consequent to all observations Many researchers such as Lilliefors (1967), Lilliefors (1969), Woodruff et al (1984), and Yen and Moore (1988) have used different test statistics to the case where parameters are unknown and to be estimated from sample. We used Newton-Raphson iterative method to obtain maximum likelihood estimates of unknown parameters of Marshall-Olkin Extended Rayleigh distribution. 3. Simulations and Power Study for Marshal-Olkin extended Rayleigh distribution We have assessed the performance of the proposed lifetime model using five important goodness of fit tests. Simulations and Power Study for Marshal-Olkin extended Rayleigh distribution We have assessed the performance of the proposed lifetime model using five important goodness of fit tests For this purpose, we have computed critical values of these goodness of fit test statistics using Monte-Carlo simulations. We have calculated power of these test statistics for MOR distribution against six competitive probability distributions
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