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

Read more

Summary

Introduction

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

Goodness of Fit Tests
The Watson Un2 test statistic is
Power study for Marshal-Olkin extended Rayleigh distribution
Conclusion
Full Text
Paper version not known

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

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.