Bayes Estimators of Exponential Parameters from a Censored Sample Using a Guessed Estimate

Abstract

INTRODUCTIONIn life testing experiments, experimenters often possess certain information about a parameter of interest, through past experience or familiarity with the experiment. The most common type of information is a probable value of the parameterθ , say 0 θ . This 0 θ has been referred in statistical literature as the point guess aboutθ .The use of the point guess for inferences regarding a parameter has been considered by many authors. Perhaps the most popular technique that utilizes the knowledge of point guess is the shrinkage technique, originally suggested by Thompson (1968). He suggested shrinking the usual estimator suggested by Pandey and Srivastava (1985) and Pandey and Upadhyay (1988). Their technique chooses a subfamily from a family of priors such that the mean of the prior distribution is equal to 0 θ . Equalization of the mean to 0 θ , however, does not seem appropriate unless the prior guess 0 θ is specified as the average value of θ . As mentioned above, prior to the sample selection, the experimenter believes that the point guess 0 θ is a possible value of the parameter. Thus, it seems more appropriate to interpret 0 θ as the most probable value rather than interpreting it as the average value of θ . Therefore, we propose that the choice of subfamily of the prior be made by equalizing the mode of the prior distribution to 0 θ . As an illustration of our proposition, we have considered the problem of estimation of the failure rate and reliability for a one-parameter exponential distribution.The exponential distribution is a widely used model in a variety of statistical procedures. Among its most prominent applications are those in the field of life testing and reliability problems.

Expected Bayesian credible limit of reliability parameters in the case of zero-failure data for exponential distribution

“…If the prior density function of λ is given by (2) according to the Bayesian theorem then the posterior density function of λ will be given…”

“…Since [1] appeared zero-failure data has been studied for more than 20 years [2] gave Bayesian estimations of failure rate and reliability with exponential distribution In order to Manuscript produce Bayesian estimations the prior to distribution was yielded in the known prior value of parameter [3] provided optimal lower confidence limits (classical confidence limit) of mean life and reliability in the case of zero-failure data for exponential distribution [4] gave the estimations and property of E-Bayesian credible limit of failure rate and reliability about zero-failure data of exponential distribution [5][6] provided the estimations of reliability parameter in the case of zero-failure using no memory property of exponential distribution [7] gave Bayesian estimation and hierarchical Bayesian estimation of failure rate on the base estimation of reliability is provided when the prior density kernel of the failure rate is the form …”

مقارنة طرائق بيز الشبه معلمية مع الطرائق التقليدية لتقدير معولية الأنظمة بإستعمال إسلوب المحاكاة

“…‫وّب‬ ‫ٚاٌّٛضؾخ‬ ‫إؽزّبٌ١خ‬ ‫وضبفخ‬ ‫ٚثذاٌخ‬ ‫األٌٚٝ‬ ‫ٌٍّشوجخ‬ ‫اٌؾ١بح‬ ‫٠أرٟ‬ : [9] x f (x; ) e , x 0, 0 [13] ‫اٌجبؽش‬ ‫لذَ‬ ‫ؽ١ش‬ Lemmer :…”

Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

“…Singh, Prakash, and Singh (2007) studied shrinkage estimators for the shape parameter of Pareto distribution using the LINEX loss function. Singh, Singh, Singh, and Upadhyay (2008) Perhaps the most popular technique that utilizes the point guess value is the shrinkage technique, originally suggested by Thompson (1968). The shrinkage estimator performs better than the usual estimator when a guess value is approximately the true value of the parameter given the sample size is small.…”