Some Properties of Past Entropy and their Applications

In the context of information theory, measure of uncertainty in past lifetime distribution has been proposed by Di Crescenzo and Longobardi (J Appl Probab 39:434–440, 2002). In this paper, we study some ordering and aging properties in terms of past entropy (based on past lifetime) and develop some characterization results. Some discrete distribution results are also addressed here.     

Proportional reversed hazard and frailty models

Reversed hazard rates are found to be very useful in survival analysis and reliability especially in study on parallel systems and in the analysis of left censored lifetime data. In this paper, we derive a class of bivariate distributions having marginal proportional reversed hazard rates. We, then, introduce a class of proportional reversed hazard rates frailty models and propose a multivariate correlated gamma frailty model. Bivariate reversed hazard rates and association measure are discussed in terms of frailty parameters.     

Multivariate survival functions characterized by constant product of mean remaining lives and hazard rates

Under the assumption that the products of multivariate mean remaining lives and hazard rates are the same constant, it is shown that the corresponding multivariate survival function belongs to one of three families: (1) multivariate Gumbel exponential distribution; (2) multivariate Lomax (Pareto type II) distribution; (3) multivariate rescaled Dirichlet distribution. This result is then used to derive another characterization of the latter two families based on the residual life distribution.     

Multivariate distributions characterized by a relationship between mean residual life and hazard rate

In this paper, we characterize some multivariate distributions based on a relationship between the multivariate hazard rate, as defined by Johnson and Kotz (1975) and Marshall (1975), and the multivariate mean residual life as defined by Arnold and Zahedi (1988). The results are extensions of the results obtained earlier by Roy (1989, 1990) and Ma (1996, 1997). Received July 1997     

On discrete α-unimodal distributions

Some characterizations of a -unimodal lattice distributions, introduced in Abouammoh (1987,19881, and a -monotone lattice distributions, introduced in Steutel (1988), are discussed. Convolution and symmetrization of a -monotone lattice distributions are also investigated. The characterizations and convolution properties obtained by Abouammoh in this connection are corrected and improved.     

On characterizing discrete distributions via conditional expectations of weak record values

Let (W _n ,n ≥ 0) denote the sequence of weak records from a distribution with support S = { α₀,α₁,...,α _N }. In this paper, we consider regression functions of the form ψ _n (x) = E(h(W _n ) |W _n+1 = x), where h(·) is some strictly increasing function. We show that a single function ψ _n (·) determines F uniquely up to F(α₀). Then we derive an inversion formula which enables us to obtain F from knowledge of ψ _n (·), ψ _n-1(·), h(·) and F(α₀).     

On estimating the reliability after sequentially estimating the mean: The exponential case

Sequential estimation problems for the mean parameter of an exponential distribution has received much attention over the years. Purely sequential and accelerated sequential estimators and their asymptotic second-order characteristics have been laid out in the existing literature, both for minimum risk point as well as bounded length confidence interval estimation of the mean parameter. Having obtained a data set from such sequentially designed experiments, the paper investigates estimation problems for the associatedreliability function. Second-order approximations are provided for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup. An ad hoc bias-corrected version is also introduced. Then, the proposed estimator is investigated further under some specific sequential sampling strategies, already available in the literature. In the end, simulation results are presented for comparing the proposed estimators of the reliability function for moderate sample sizes and various sequential sampling strategies.     

On estimating the mean of the selected normal population under the LINEX loss function

Following Parsian and Farsipour (1999), we consider the problem of estimating the mean of the selected normal population, from two normal populations with unknown means and common known variance, under the LINEX loss function. Some admissibility results for a subclass of equivariant estimators are derived and a sufficient condition for the inadmissibility of an arbitrary equivariant estimator is provided. As a consequence, several of the estimators proposed by Parsian and Farsipour (1999) are shown to be inadmissible and better estimators are obtained. Received January 2001/Revised May 2002     

Estimation of the mean of the selected population under asymmetric loss function

This paper is concerned with the comparison of seven estimators of the mean of the selected population from two normal populations with unknown means and common known variance under an asymmetric loss namely the LINEX loss function. The proposed estimators are invariant under location transformation. The bias and risks of the seven estimators are computed and compared. The conclusion recommend the use of δ_P (σ) which is simple to use and it is minimax. Received: January 1999     

On truncated bivariate discrete distributions: A unified treatment

A unified treatment of three types of zero class truncation for bivariate discrete distributions is presented. Using the probability generating function approach, various properties of the truncated distributions are examined in association with the corresponding properties of the initial complete form of the distribution. Expressions for moments and conditional distributions are also obtained. Bivariate versions of the Thomas and the Intervened Poisson distributions are introduced and used as illustrative examples. Received November 2000/Revised March 2002     

Quantile-locating functions and the distance between the mean and quantiles

Given a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p -quantile of X and its mean in terms of the central absolute first moment of X . The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.     

On the Lp error of the Grenander-type estimator in the Cox model

We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for L_p-error of the Grenander-type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the L_p-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.     

土地还原率的误差传播

由于土地还原利率在理论和计算上的复杂性,往往不可避免地出现混乱定值,使得收益法评估在评估地价时失效,这就有必要对其精度进行评定。本文用定量的方式,采用误差传播律,分别对综合还原利率、租价比方法、安全利率加风险调整法、复合投资收益率法、投资收益率排序插入法的土地还原率求取进行精度评估,得出衡量还原率精度的指标。其作用在于对评估过程进行全程质量估计和控制,有利于约束和规范评估方法。     

On the value of information in the presence of moral hazard

This paper shows that the marginal value of a “small amount of non-output information” is generally non-positive in the context of the standard principal-agent model involving moral hazard, which suggests a non-concavity in the value of information. However, when both the principal and the agent are risk neutral, even a small amount of non-output information may exhibit a positive incremental value in presence of a liability constraint.      

On characterizations of distributions by expected values of order statistics and record values with gap

In this paper, we obtain some recurrence relationships for conditional expectations of nonadjacent order statistics and record values when the distribution function is absolutely continuous, and we prove that the distribution function is uniquely determined by the distribution of conditioned record values and by the expected values of these records. Further, different distributions are characterized by these relationships.     

On discrimination in the optimal management of teams

We study the optimal management of teams in which agents’ effort decisions are mapped (via a production technology) into the probability of the team’s success. Optimal wage schemes in such context are largely discriminatory, but we show that the extent of the discrimination crucially depends on the existence of moral hazard. More precisely, for teams with a flat structure, the domain of production technologies giving rise to discrimination is broader when agents’ actions are observable and contractible. For teams with a sequential structure, the result reverses and the domain of production technologies giving rise to discrimination is broader when there exists moral hazard. Finally, in more cooperative environments in which agents are allowed to collude, optimality does not entail discrimination, with or without moral hazard.     

Record values of the Lomax distribution

In this paper, firstly an introduction to the idea of record values for a sequence of independent and identically (Lomax or Pareto II) distributed random variables is given. Some of the distributional properties of these record values and moments up to second order are derived. These moments clearly depend on the location, scale and shape parameter of the Lomax distribution and two types of estlmators of these parameters, based on a series of observed record values are presented.     

浅析高压气流引射防尘雨幕在煤矿安全生产中的应用

矿尘始终是困扰井下安全生产的最大因素之一。长期从事采掘和粉尘作业环境的职工,易引起尘肺病,在高度粉尘作业场所工作的职工,视线易受阻挡,操作中易造成人身事故。其最大危害在于煤尘具有爆炸危险的矿井,煤尘在一定的条件下易发生煤尘爆炸事故,给矿井安全生产带来很大威胁。     

Evaluation of P(Xt>Yt ) when both Xt and Yt are residual lifetimes of two systems

Let the random variables X and Y denote the lifetimes of two systems. In reliability theory to compare between the lifetimes of X and Y there are several approaches. Among the most popular methods of comparing the lifetimes are to compare the survival functions, the failure rates and the mean residual lifetime functions of X and Y. Assume that both systems are operating at time t > 0. Then the residual lifetimes of them are X_t=X?t | X>t and Y_t=Y?t | Y>t, respectively. In this paper, we introduce, by taking into account the age of systems, a time‐dependent criterion to compare the residual lifetimes of them. In other words, we concentrate on function R(t ):=P(X_t>Y_t) which enables one to obtain, at time t, the probability that the residual lifetime X_t is greater than the residual lifetime Y_t. It is mentioned, in Brown and Rutemiller (IEEE Transactions on Reliability, 22 , 1973) that the probability of type R(t) is important for designing as long‐lived a product as possible. Several properties of R(t) and its connection with well‐known reliability measures are investigated. The estimation of R(t) based on samples from X and Y is also discussed.     

Goodness-of-fit tests for discrete models based on the integrated distribution function

This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between the integrated distribution function Ψ(t)=∫_t ^∞ (1−F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for small samples and exhibits high power with respect to competitive procedures over a large range of alternatives. Received: July 1998