Double stage shrinkage estimator of two parameters generalized exponential distribution

Abstract

This paper is concerned with double stage shrinkage estimator (DSSE) for lowering the mean squared error of classical estimator (MLE) for the shape parameter (α) of generalized Exponential (GE) distribution in a region (R) around available prior knowledge (α 0 ) about the actual value (α) as initial estimate in case when a scale parameter (λ) is known as well as to reduce the cost of experimentations.In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor ψ(⋅) and for acceptance mentioned region R.Expressions for Bias, Mean square error (MSE), Expected sample size [E(n/α,R)], Expected sample size proportion [E(n/α,R)/n], probability for avoiding the second sample

Single Stage Shrinkage Estimation Methods for Reliability Function of Generalized Exponential Distribution Using Simulation

“…The term stress-strength (s-s) refers to a component that has a random strength X subject to a random stress Y to evaluate reliability, A failure occurs in the simplest form of the stressstrength model when the unit's strengths drop below the stress. Then, we will study two models as follows; 1-The series system reliability Rs for (s-s) model [1], [2] and [3] Many researchers studied the parallel and series of system reliability in the stress-strength model. For example, in 1996, Hanagal studied the reliability consist many parallel components and two strength that belongs to bivariate Petro [6].…”

“…In 2013, Alaa estimated stress-strength reliability for a parallel system using Lomax distribution. In 2018, Cheng demon started the reliability of the system in the (s-s) model of parallel components based on the Pareto exponential distribution [1]. On the other hand, the generalized exponential distribution denoted by (GED) is also known as two parameters was important distribution with extensive uses in all tests of life as it enters in the tests of population growth, and engineering.…”