Open AccessEstimation Based on Optimally Selected Single Order Statistic in Pareto: Rayleigh Distribution
Author(s) -
M. Ravikumar,
I. Narasimha Rao,
R. R. L. Kantam
Publication year - 2022
Publication title -
international journal for research in applied science and engineering technology
Language(s) - English
Resource type - Journals
ISSN - 2321-9653
DOI - 10.22214/ijraset.2022.40903
Subject(s) - statistic , rayleigh distribution , mathematics , statistics , pareto distribution , order statistic , pareto principle , parametric statistics , variance (accounting) , probability density function , economics , accounting
Abstract: A special case of the well known T – X family of distributions proposed by Ayman Alzaatreh et al. (2012) called Pareto – Rayleigh (P – R) distribution is considered. Its scale parameter is estimated using a single order statistic in small samples. Optimal criterion for the choice of single order statistic in a given small sample is worked out. Comparison is made with the corresponding optimal choice of single order statistic with respect to the criterion of asymptotic variance. The results are extended to estimate parametric functions like reliability and hazard rate. Keywords: T-X family, Pareto-Rayleigh distribution, order statistics, optimal estimation, asymptotic variance.