Comparing parameters and Reliability of two-parameters exponential

Abstract

One of the most important problems in the statistical inference is estimating parameters and Reliability parameter and also interval estimation , and testing hypothesis . estimating two parameters of exponential distribution and also reliability parameter in a stress-strength model. This parameter deals with estimating the scale parameter and the Location parameter µ , of two exponential distribution ,using moments estimator and maximum likelihood estimator , also we estimate the parameter R=pr(x>y), where x,y are two- parameter independent exponential random variables .Statistical properties of this distribution and its properties is studied , and simulation procedure is used to find estimators using four set of initial values of parameters were found ) for different sample size (n=10,25,50,75,100) L=500 , and the results are compared using mean square error offer that the parameter R is also estimated and compared using MSE . the results are explained in tables .