A class of efficient and modified testimators for the mean of normal distribution using complete data

On Shrinkage Estimation for R(s, k) in Case of Exponentiated Pareto Distribution

“…As Thompson suggested in (1968), the shrinkage estimator of α denoted by (α ) is defined as below: α ∅ α α 1 ∅ α α (13) He shrinks a usual estimator to prior information using shrinkage weight factor ∅ α and he believed is closed to α [5], [7]. We apply the unbiased estimator as a usual estimator and as a prior information of α in this paper.…”

“…The model mentioned used in many applications in physics and engineering and many authors had studied and estimated R(s,k)for example: Afify in (2010), showed that the Exponentiated Pareto distribution denoted by EP (α, λ) used quite successfully in studying many lifetime data and the EP ( , λ) decreasing and upside-down bathtub shaped failure rates depending on shape parameter α [2]. Hassan& Basheikh in (2012), estimated , using Bayes and non-Bayes estimation methods when the strength and stress are non-identical and follows the Exponentiated Pareto distribution [3], Rao et al in (2016), estimated the reliability system in a multicomponent stress-strength when stress and strength follows Exponentiated Weibull distribution for different shape parameters [4], and in (2017) Abbas and Fatima, they estimated the reliability of the multicomponent system in stress-strength model for Exponentiated Weibull distribution, using; ML, MOM and the conclude results approved that the Shrinkage estimator using Shrinkage weight function was the best [5].…”

Two modified estimators of reliability function with exponential failure model based on prior information and time-censored data

“…A ready-made answer is given through the use of the preliminary test shrunken (PTS) procedure, which assures utilizing u o in new estimation problems of u and R(t), getting the estimators easily and quickly and working on improving the quality of the estimators. 15,16 The conventional PTS, the estimator of u, is defined as follows: let T i , i = 1, 2, . .…”

“…Several authors have studied the PTS estimator for the parameter u of exponential distribution or normal distributions for complete, type I and type II censored data by choosing different k and R. 9,[11][12][13][17][18][19][20][21][22][23][24] One may refer to Al-Hemyari and Husain, 15 Al-Hemyari et al, 16 Chiou 18 and Al-Hemyari and Al-Dolami 25 for further discussions and in different directions.…”

“…The optimum value of k that minimizes the risk depends on the unknown parameter u, and therefore, it has to be estimated from the censored data. The expression of k and thenk is too complicated, 15,16 which is one of the limitations of this procedure. Thus, empirical choice of k is recommended.…”