A note on the conditional residual lifetime of a coherent system under double monitoring

In this note, we derive some mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at time t₁ the jth failures has occurred and at time t₂ the kth failures (j < k) have not occurred yet. Based on the mixture representations, we then discuss the stochastic comparisons of the conditional residual lifetimes of two coherent systems with i.i.d. components.     

Ordering properties of sample minimum from Kumaraswamy-G random variables

In this paper we compare the minimums of two independent and heterogeneous samples each following Kumaraswamy (Kw)-G distribution with the same and the different parent distribution functions. The comparisons are carried out with respect to usual stochastic ordering and hazard rate ordering with majorized shape parameters of the distributions. The likelihood ratio ordering between the minimum order statistics is established for heterogeneous multiple-outlier Kw-G random variables with the same parent distribution function.     

The power piecewise exponential model

In this paper an extension of the piecewise exponential distribution based on the distribution of the maximum of a random sample is considered. Properties of its density and hazard function are investigated. Maximum likelihood inference is discussed and the Fisher information matrix is identified. Results of two real data applications are reported, where model fitting is implemented by using maximum likelihood. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models.     

Necessary and sufficient conditions for stochastic orders between (n − r + 1)-out-of-n systems in proportional hazard (reversed hazard) rates model

Consider two (n ? r + 1)-out-of-n systems, one with independent and non-identically distributed components and another with independent and identically distributed components. When the lifetimes of components follow the proportional hazard rates model, we establish a necessary and sufficient condition for the usual stochastic order to hold between the lifetimes of these two systems. For the special case of r = 2, some generalized forms of this result to the hazard rate, dispersive and likelihood ratio orders are also obtained. Moreover, for the case when the lifetimes of components follow the proportional reversed hazard rates model, we derive some similar results for comparing the lifetimes of two systems . Applications of the established results to different situations are finally illustrated.     

青岛市外来劳动人口调查

如何解决沿海城市不断涌入的外来劳动人口和本地劳动人口的就业问题,是我国城镇化发展过程中一些区域中心城市面临的共同难题。基于对近年青岛市外来劳动人口状况的调查,基本摸清了该城市外来劳动人口的主要特点,分析阻碍吸纳外来劳动人口的原因。根据"敞开大门、城乡兼顾、平等对待、有序流动"的原则,提出改善管理、缓解就业压力的政策建议。     

LIMIT THEOREMS FOR PROPORTIONS OF OBSERVATIONS FALLING INTO RANDOM REGIONS DETERMINED BY ORDER STATISTICS

In this paper, we study asymptotic behavior of proportions of sample observations that fall into random regions determined by a given Borel set and an order statistic. We show that these proportions converge almost surely to some population quantities as the sample size increases to infinity. We derive our results for independent and identically distributed observations from an arbitrary cumulative distribution function, in particular, we allow samples drawn from discontinuous laws. We also give extensions of these results to the case of randomly indexed samples with some dependence between observations.     

Topp–Leone normal distribution with application to increasing failure rate data

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.     

世界男子跳水运动员难度动作位序分析——以第29届奥运会男子单人10米台跳水决赛为例

运用图像分析法、文献资料法、数理统计法等研究方法,对第29届奥运会男子单人跳水决赛前8名运动员难度动作出现的位序与成绩关系进行分析。研究表明,整套难度动作位序布局的合理性、难度系数动作类别组编的均衡性与运动成绩呈正相关,难度动作的选择应与运动员的实际身体素质水平和专业技术水平相吻合,动作才能完成得轻松优美,才能充分展现男子单人10米跳台运动员的个性化特点,难与美的结合仍然是当今跳水制胜的关键。