Saima Naqash; S.P Ahmad; Aquil Ahmed

Bayesian Approach to Generalized Normal Distribution under Non-Informative and Informative Priors

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Author(s)

Saima Naqash ^1,* S.P Ahmad ¹ Aquil Ahmed ²

1. Department of Statistics, University of Kashmir Srinagar, J&K, 190006 State, India

2. Department of Statistics & O.R, Aligarh Muslim University Aligarh, UP, India

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2018.04.02

Received: 30 Mar. 2018 / Revised: 13 Apr. 2018 / Accepted: 11 May 2018 / Published: 8 Nov. 2018

Index Terms

Generalized Normal distribution, Newton-Raphson method, incomplete gamma function, joint posterior distribution, Fisher Information, Lindley approximation, Mean square error

Abstract

The generalized Normal distribution is obtained from normal distribution by adding a shape parameter to it. This paper is based on the estimation of the shape and scale parameter of generalized Normal distribution by using the maximum likelihood estimation and Bayesian estimation method via Lindley approximation method under Jeffreys prior and informative priors. The objective of this paper is to see which is the suitable prior for the shape and scale parameter of generalized Normal distribution. Simulation study with varying sample sizes, based on MSE, is conducted in R-software for data analysis.

Cite This Paper

Saima Naqash, S.P.Ahmad, Aquil Ahmed,"Bayesian Approach to Generalized Normal Distribution under Non-Informative and Informative Priors", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.4, No.4, pp.19-33, 2018. DOI: 10.5815/ijmsc.2018.04.02

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International Journal of Mathematical Sciences and Computing (IJMSC)