Abstract
In this paper we proposed Bayes estimators for complete sample of the Modified InverseRayleigh (MIR) parameters which was introduced by Khan (2014). Different approximationmethods with squared error loss function (SELF) have been used to develop the bayesestimators for the unknown parameters. The proposed estimators are compared with the correspondingmaximum likelihood estimators by simulation study on the basis of mean squareerror (MSE). To illustrate the usefulness and goodness of fit of Modified Inverse Rayleighdistribution we considered two real data sets.
Highlights
The two parameter Modified Inverse Rayleigh (MIR) distribution is a generalization of the Inverse Rayleigh distribution
In our literature we consider T-K approximation (Tierney and Kadanes’s), Lindley’s approximation method and Markov Chain Monte Carlo (MCMC) approximation method and these methods are used to solve integral problems and a single numerical result is obtained from these techniques
Bayes estimators are developed using informative priors as well as non-informative priors. It can be observed from table 1 that when we used informative prior the mean square error (MSE)’s of bayes estimates for both parameters using Lindley’s approximation is less than as compared to Mean Square Errors (MSE’s) of maximum likelihood estimates
Summary
The two parameter MIR distribution is a generalization of the Inverse Rayleigh distribution. This distribution was discussed by Khan (2014). He studied its some mathematical properties along with the estimation of its parameters. It is to be noted that in different literatures, authors only discussed the statistical properties and classical estimation i.e. maximum likelihood estimates of the Modified Inverse Rayleigh (MIR) distribution.
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