Bayesian prediction of future number of failures based on finite mixture of general class of distributions

This paper is concerned with the Bayesian prediction problem of the number of components which will fail in a future time interval. The failure times are distributed according to a finite mixture of a general class of distributions. Type-I censored sample from this nonhomogeneous population and a general class of prior density functions are used. A one-sample scheme is used to predict the number of failures in a future time interval. An example of a finite mixture of k exponential components is given to illustrate our results.     

Reliability Properties of Reversed Residual Lifetime

Abstract

If the random variable X denotes the lifetime (X ≥ 0, with probability one) of a unit, then the random variable X _t  = (t ? X|X ≤ t), for a fixed t > 0, is known as `time since failure', which is analogous to the residual lifetime random variable used in reliability and survival analysis. The reversed hazard rate function, which is related to the random variable X _t , has received the attention of many researchers in the recent past [(cf. Shaked, M., Shanthikumar, J. G., 1994 Shaked, M. and Shanthikumar, J. G. 1994. Stochastic Orders and Their Applications New York: Academic Press.  [Google Scholar]). Stochastic Orders and Their Applications. New York: Academic Press]. In this paper, we define some new classes of distributions based on the random variable X _t and study their interrelations. We also define a new ordering based on the mean of the random variable X_t and establish its relationship with the reversed hazard rate ordering.     

Selection of suitable prior for the Bayesian mixture of a class of lifetime distributions under type-I censored datasets

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration.     

MRL and MPL Functions of Parallel Systems with INID Components under Double Monitoring

This article investigates parallel systems with n independent but not identically distributed (INID) components. Under the condition that, at time t ₁ (t ₁ > 0) the total number of failures of the components is r (r < n), and at time t ₂ (t ₂ ≥ t ₁) the sys-tem is still working or it has failed, the mean residual life (MRL) function of the parallel system and the mean past lifetime (MPL) function of the components are conducted. Some representations and corresponding properties of the MRL function and the MPL function under several specific conditions are obtained.     

Some New Bounds on the Probability of Extinction of a Galton–Watson Process with Numerical Comparisons

Some new upper and lower bounds for the extinction probability of a Galton–Watson process are presented. They are very easy to compute and can be used even if the offspring distribution has infinite variance. These new bounds are numerically compared to previously discussed bounds. Some definite guidelines are given concerning when these new bounds are preferable. Some open problems are also discussed.     

Characterizations Based on Cumulative Residual Entropy of First-Order Statistics

Two different distributions may have equal cumulative residual entropy (CRE), thus a distribution cannot be determined by its CRE. In this article, we explore properties of the CRE and study conditions under which the CRE of the first-order statistics can uniquely determines the parent distribution. Weibull family is characterized through ratio of the CRE of the first-order statistics to its expectation. We have also some bounds for the CRE of residual lifetime of a series system.     

Lifetime mating success of males in a natural population of the papilionid butterfly,Atrophaneura alcinous (Lepidoptera: Papilionidae)

Summary Lifetime mating success of males in a natural population of the papilionid butterfly,Atrophaneura alcinous, was investigated and causes of the variation were examined. The most successful males mated with 5 females, whereas about 73% of the males failed to mate. Body size of males was not correlated with their eclosion date, longevity and lifetime mating success. There was no trade-off between mating success and longevity, and long-lived males had a disproportionately high mating success. Although number of available females per male per day was not variable among males with different longevities, long-lived males had higher mating efficiency. Time interval between matings by non-virgin males was shorter than that from eclosion to the first mating. High lifetime mating success of long-lived males was strongly related to their mating experience, not to their ageper se.     

Life Expectancy,Schooling, and Lifetime Labor Supply: Theory and Evidence Revisited

This paper presents a theoretical and empirical analysis of the role of life expectancy for optimal schooling and lifetime labor supply. The results of a simple prototype Ben‐Porath model with age‐specific survival rates show that an increase in lifetime labor supply is not a necessary, or a sufficient, condition for greater life expectancy to increase optimal schooling. The observed increase in survival rates during working ages that follows from the “rectangularization” of the survival function is crucial for schooling and labor supply. The empirical results suggest that the relative benefits of schooling have been increasing across cohorts of U.S. men born between 1840 and 1930. A simple quantitative analysis shows that a realistic shift in the survival function can lead to an increase in schooling and a reduction in lifetime labor hours.     

大学生终身体育锻炼能力培养初探

如何培养大学生终身体育锻炼意识和能力,是高校体育教学的重要任务之一。本文重点从六个方面进行论述。     

全面建设小康社会·高等教育大众化·终身教育

全面建小康、高等教育大众化、终身教育是与新世纪中国社会、经济、教育密切关联的诱人景观,三者之间存在必然联系:全面建小康包含高等教育大众化提升大众文化品质的目标追求;高等教育大众化是全面建小康的必要构成;终身教育是二者的必然归宿。三者目标相接,精神相通,过程相依,应相互关注,共同构建通向学习型社会的桥梁。