Abstract
This article is concerned with the problem of estimating the parameters, reliability and hazard rate functions of the mixture of two Rayleigh distributions ($MTRD$) based on generalized order statistics ($GOS$). The maximum likelihood and Bayes methods of estimation are used for this purpose. The Markov chain Monte Carlo ($MCMC$) method is used for obtaining the Bayes estimates under the squared error loss and $LINEX$ loss functions. Our results are specialized to progressive Type-II censored order statistics and upper record values. Comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.
Highlights
The Rayleigh distribution (RD) was first derived by Lord Rayleigh in connection with a study of acoustical problems
This article is concerned with the problem of estimating the parameters, reliability and hazard rate functions of the mixture of two Rayleigh distributions (MT RD) based on generalized order statistics (GOS )
Our results are specialized to progressive Type-II censored order statistics and upper record values
Summary
The Rayleigh distribution (RD) was first derived by Lord Rayleigh in connection with a study of acoustical problems. The RD is used to model wave heights in oceanography, and in communication theory to describe hourly median and instantaneous peak power of received radio signals. Several such situations have been discussed by Polovko (1968), Takeshi Yamane (1998), Zhi Ren et al (2011), and many others. The RD is a special case of two parameter Weibull distribution. A random variable T is said to have a RD with parameter θ if its probability density function (PDF) is given by f (t) = 2θ t e−θt , t > 0, (θ > 0)
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