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S.P. Ahmad
Afaq Ahmad
A. Ahmed
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Afaq Ahmad
A. Ahmed
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International Journal of Statistics and Mathematics IF 2015: 4.232

Bayesian analysis of shape parameter of Lomax distribution using different loss functions

Afaq Ahmad, S.P. Ahmad and A. Ahmed

Accepted 12 January, 2015.

Citation: Afaq A, SP Ahmad, Ahmed A (2015). Bayesian analysis of shape parameter of Lomax distribution using different loss functions. Int. J. Stat. Math., 2(1): 055-065.

Copyright: © 2015 Ahmad et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Abstract

The Lomax distribution also known as Pareto distribution of the second kind or Pearson Type VI distribution has been used in the analysis of income data, and business failure data. It may describe the lifetime of a decreasing failure rate component as a heavy tailed alternative to the exponential distribution. In this paper we consider the estimation of the parameter of Lomax distribution. Baye’s estimator is obtained by using Jeffery’s and extension of Jeffery’s prior by using squared error loss function, Al-Bayyati’s loss function and Precautionary loss function. Maximum likelihood estimation is also discussed. These methods are compared by using mean square error through simulation study with varying sample sizes. The study aims to find out a suitable estimator of the parameter of the distribution. Finally, we analyze one data set for illustration.

Keywords: Lomax distribution, Bayesian estimation, priors, loss functions, fisher information matrix.