Abstract
In this study, the shape parameter of the weighted Inverse Maxwell distribution is estimated by employing Bayesian techniques. To produce posterior distributions, the extended Jeffery's prior and the Erlang prior are utilised. The estimators are derived from the squared error loss function, the entropy loss function, the precautionary loss function, and the Linex loss function. Furthermore, an actual data set is studied to assess the effectiveness of various estimators under distinct loss functions.
Highlights
The estimation of parameters of weighted inverse Maxwell distribution is obtained by using the method of maximum likelihood estimation
Application This section provides an application that assesses the efficacy of estimators and the posterior risk of various loss functions
According to decision rule of less Bayes posterior risk, we accomplish that Linex error loss function is more useful than others
Summary
Boltzmann, is a continuous probability distribution that underpins the kinetic energy of gases as well as their indispensable characteristics such as pressure and diffusion. This distribution is known as the distribution of velocities, energy and magnitude of momenta of molecules. Let denotes a random variable from Maxwell distribution, the transformation = is said to follow inverse of Maxwell distribution having probability function (pdf) given by. Ahmad et al [3], studied the weighted analogue of inverse Maxwell distribution. Figures (1.1) and (1.2) represent some layouts of weighted inverse Maxwell distribution for distinct values of parameters. Bayesian Estimation of Weighted Inverse Maxwell Distribution
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