Preliminary Test and ‎‎Shrinkage Estimations of Scale Parameters for Two Exponential Distributions based on Record Values

Abstract

The exponential distribution is applied in a very wide variety of statistical procedures.Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or use the individual sample. In this paper, the preliminary test estimator and shrinkage estimator are studied. The optimum level of significance for preliminary test estimation and the optimum values of shrinkage coefficient are obtained based on minimax regret criterion under the weighted square error loss function.

Estimation of Stress Strength Reliability P [Y < X < Z] of Lomax Distribution under Different Sampling Scheme

“…[31] has found the shrinkage estimate of the parameters of exponential distribution. [32], [33], [34] obtain the Shrinkage estimation in the context of exponential distribution. [35] obtained the shrinkage estimator of stress strength reliability R = P [X < Y ] when X and Y are geometric distributions using record values.…”

Rayleigh Confidence Regions based on Record Data

“…For more details, see Nevzorov (1988), Ahsanullah (1995) and Arnold et al (1998). For some recent references, see Asgharzadeh et al (2013), Mirfarah and Ahmadi (2014) and Zakerzadeh et al (2016).…”