Bayes Estimation Based on Joint Progressive Type II Censored Data Under LINEX Loss Function

In the lifetime experiments, the joint censoring scheme is useful for planning comparative purposes of two identical products manufactured coming from different lines. In this article, we will confine ourselves to the data obtained by conducting a joint progressive Type II censoring scheme on the basis of the two combined samples selected from the two lines. Moreover, it is supposed that the distributions of lifetimes of the two products satisfy in a proportional hazard model. A general form for the distributions is considered, and we tackle the problem of obtaining Bayes estimates under the squared error and linear-exponential (LINEX) loss functions. As a special case, the Weibull distribution is discussed in more detail. Finally, the estimated risks of the various estimators obtained are compared using the Monte Carlo method.     

On the Similarity Structure of Order Statistics

In this article, we address the similarity structure between pairs of order statistics of an identically distributed independent random variables X₁,…, X_n. The overlapping coefficient (Δ) of Weitzman (1970 Weitzman , M. S. ( 1970 ). Measures of overlap of income distributions of white and Negro families in the United States . Technical Paper No. 22 , Washington , D.C. , U.S.A : Department of Commerce, Bureau of Census . [Google Scholar]), is used to assess the degree of similarity or closeness between pairs of order statistics. It appears that the degree of the similarity between any of such pairs is independent of the parent distribution. Using this notion, it is shown that for i < j, the degree of similarity between distributions of the ith and the jth order statistics decreases as i and j sunder. Some possible biometric applicability of the value of Δ are explored. In particular, the use of this measure in estimation of the number of possible strata, subgroups or natural subdivisions in a population are suggested.     

Inequalities for Expected Current Record Statistics

In this article, we obtain sharp distribution-free bounds for the expected value of the gap between the current records and record values as well as upper sharp bounds for the spacings between any two upper current records. We also present two-sided bounds on the errors in approximating the means of current records by inverse hazard functions.     

General treatment of goodness-of-fit tests based on Kullback–Leibler information

This paper introduces a general goodness-of-fit test based on the estimated Kullback–Leibler information. The test uses the Vasicek entropy estimate. Two special cases of the test for location–scale and shape families are discussed. The results are used to introduce goodness-of-fit tests for the uniform, Laplace, Weibull and beta distributions. The critical values and powers for some alternatives are obtained by simulation.     

Generalized exponential distribution: Moments of order statistics

In this paper, we consider the generalized exponential distribution (GED) with shape parameter α. We establish several recurrence relations satisfied by the single and the product moments for order statistics from the GED. The relationships can be written in terms of polygamma and hypergeometric functions and used in a simple recursive manner in order to compute the single and the product moments of all order statistics for all sample sizes.     

Some results on the mean residual waiting time of records

Often, in reliability theory, risk analysis, renewal processes and actuarial studies, mean residual life function or life expectancy plays an important role in studying the conditional tail measure of lifetime data. In this paper, we introduce the notion of the mean residual waiting time of records and present some monotonic and aging properties. Sharp bounds for the mean residual waiting time of records are also investigated.     

On the efficiency of monte carlo methods using steady state ranked simulated samples

Samawi (1999) showed that the efficiency of Monte Carlo methods of integrals estimation can be substantially improved by using ranked simulated samples (RSIS) in place of uniform simulated samples (USIS). However, in this paper it is shown that substantial improvement of efficiency can be achieved further by using the steady state ranked simulated sample (SRSIS). It appears that the modified Monte Carlo methods using SRSIS provide unbiased and more efficient estimators for the integrals. Some theoretical properties of SRSIS are given. A simulation study is conducted to compare the performance of the methods using SRSIS with respect to USIS, for some examples.     

A note on Pitman's measure of closeness with balanced loss function

In this note, we consider the problem of estimating an unknown parameter θ in the sense of the Pitman's measure of closeness (PMC) using the balanced loss function (BLF). We show that the PMC comparison of estimators under the BLF can be reduced to the PMC comparison under the usual absolute error loss. The Pitman-closest estimators of the location and scale parameters under BLF are also characterized. Illustrative examples are given to show the broad range applications of the obtained results.     

Social Protection Spending in Context of Structural and Institutional Performance: A Global Empirical Analysis

Social Indicators Research - An understanding about the dynamics of social protection spending is made in the context of structural and institutional performances. A dataset of 134 countries for...     

Water cycle algorithm for solving the reliability-redundancy allocation problem with a choice of redundancy strategies

Abstract

This paper proposes a new mathematical model for the reliability-redundancy allocation problem (RRAP) with a choice of redundancy strategies. To maximize the reliability of a system, this model chooses the best redundancy strategy from among both active and standby ones for each subsystem. For those with a standby strategy, a continuous time Markov chain model is used to calculate the exact reliability values. In order to solve the proposed mixed-integer non-linear programing model, a powerful evolutionary algorithm, called water cycle algorithm (WCA), is developed and implemented on three famous benchmark problems. Finally, the results of different benchmark problems are compared with those previously reported to show the superiority of the proposed model and the efficiency of WCA.