Open AccessEstimation of density and distribution functions of a Burr X distribution
Author(s) -
Amulya Kumar Mahto,
YOGESH MANI TRIPATH,
Sanku Dey
Publication year - 2018
Language(s) - English
DOI - 10.47302/jsr.2018520103
Subject(s) - mathematics , statistics , percentile , mean squared error , cumulative distribution function , estimation , monte carlo method , probability density function , engineering , systems engineering
Burr type X distribution is one of the members of the Burr family which was originally derived by Burr (1942) and can be used quite effectively in modelling strength data and also general lifetime data. In this article, we consider efficient estimation of the probability density function (PDF) and cumulative distribution function (CDF) of Burr X distribution. Eight different estimation methods namely maximum likelihood estimation, uniformly minimum variance unbiased estimation, least square estimation, weighted least square estimation, percentile estimation, maximum product estimation, Cremer-von-Mises estimation and Anderson-Darling estimation are considered. Analytic expressions for bias and mean squared error are derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set has been analyzed for illustrative purposes.