The mean residual of record values at the level of previous records

In the study of reliability of the technical systems, records model plays an important role. Suppose that a technical system is subject to shocks, e.g. peaks of voltages or stresses. The successive large shocks may be viewed as realizations of records from a sequence of identically independent voltages. Assume that the lower limit value of the mth record voltage (stress) is v > 0. Under these conditions, we propose a mean residual of records (MRR’s) for the future records. We study several properties of MRR. We show that the proposed MRR uniquely characterizes the distribution function that generated the sequence of records. It is proved that when the model under study has an increasing hazard rate the corresponding MRR is decreasing. We also compare between two record systems based on their MRR’s when these systems are ordered in terms of their hazard rates.     

Some results on residual entropy function

Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the Shannon residual entropy function as a useful dynamic measure of uncertainty. They studied the characterization problem from the residual entropy. They also used this function to define a stochastic order and two classes of distributions, DURL and IURL. In this paper, we obtain some new results on this function and we correct some mistakes in the preceding literature.Supported by Ministerio de Ciencia y Tecnologia under grant BFM2000-0362Acknowledgements. We thank two anonymous referees for some useful comments that led to an improvement in the presentation of this paper.     

Precedence-type tests based on record values

Precedence-type tests based on order statistics are simple and efficient nonparametric tests that are very useful in the context of life-testing, and they have been studied quite extensively in the literature; see Balakrishnan and Ng (Precedence-type tests and applications. Wiley, Hoboken, 2006). In this paper, we consider precedence-type tests based on record values and develop specifically record precedence test, record maximal precedence test and record-rank-sum test. We derive their exact null distributions and tabulate some critical values. Then, under the general Lehmann alternative, we derive the exact power functions of these tests and discuss their power under the location-shift alternative. We also establish that the record precedence test is the uniformly most powerful test for testing against the one-parameter family of Lehmann alternatives. Finally, we discuss the situation when we have insufficient number of records to apply the record precedence test and then make some concluding remarks.     

On the Fisher information in record values

In this article, we establish some general results concerning the comparison of the amount of the Fisher information contained in n record values with the Fisher information contained in n iid observations from the original distribution. Some common distributions are classified according to this criterion. We also propose some methods of estimation based on record values. The results may be of interest in some life testing problems. Received: September 1999     

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.     

Characterizations of bivariate distributions using concomitants of record values

In this paper, we consider a family of bivariate distributions which is a generalization of the Morgenstern family of bivariate distributions. We have derived some properties of concomitants of record values which characterize this generalized class of distributions. The role of concomitants of record values in the unique determination of the parent bivariate distribution has been established. We have also derived properties of concomitants of record values which characterize each of the following families viz Morgenstern family, bivariate Pareto family and a generalized Gumbel’s family of bivariate distributions. Some applications of the characterization results are discussed and important conclusions based on the characterization results are drawn.     

Characterization of exponential distribution via regression of one record value on two non-adjacent record values

We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the other next to the fixed record value, and none of them are adjacent. In particular, it turns out that the underlying distribution is exponential if and only if given the first and last record values, the expected value of the median in a sample of record values equals the sample midrange.     

Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543–547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.     

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).     

Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector

We consider estimation of the mean vector, $\theta $ , of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non decreasing Laplacian of the form $\pi (\Vert \theta \Vert ^{2})$ , under certain conditions on the generating function $f(\cdot )$ of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.     

Irreversibility and entropy

The genesis and role of entropy in statistical thermodynamics are discussed from first principles, showing in what respect the H-function is unique. Simplifications are introduced in the theory of fluctuations and diverse, often misleading, definitions of entropy are reconciled. The discussion is kept throughout accessible to the non-physicists.     

Generalized P‐values and Bayesian evidence in the one‐sided testing problems under exponential distributions

The problem of comparing the frequentist evidence and the Bayesian evidence in the one‐sided testing problems has been widely treated and many researches revealed that these two methods can reach an agreement approximately. However, most of the previous work dealt mainly with situations without nuisance parameters. Since the presence of nuisance parameters is very common in practice, whether these two kinds of evidence still reach an agreement is a problem worthy of study. In this article, we establish in a systematic way under the exponential distributions the agreement of the Bayesian evidence and the generalized frequentist evidence (the generalized P‐value) for a variety of one‐sided testing problems where the nuisance parameters are involved.     

Approximation for the cumulative and inverse gamma distribution

The gamma distribution function can be expressed in terms of the Normal distribution and density functions with sufficient accuracy for most practical purposes.
The distribution function for the density x^Λ-1e^-x/μ/μ^ΛΓ(A) on 0 -R(Λ){(1 + 1/1 2Λ) φ(z) + 11 -z/4Λ^1/2+2(z²+ 2)/45Λ] φ(z) /3 Λ^1/2} where φ(z)≅1/[1 +_e^{-2z(√2/π+z2 /28)}] and φ(z) = e^{-z2 /2}/√2π are the Normal distribution and density functions, y is the appropriate root of y-y²/6+y³/36-y⁴/270= In (x/Λμ), z= Λ^1/2 y, and R( Λ) is the remainder term in Stirling's approximation for In Γ(Λ).     

Ordering univariate distributions by entropy and variance

This paper examines the role of variance and entropy in ordering distributions and random prospects. There is no universal relation between entropy and variance orderings of distributions. But we place their relationship in the context of a stronger ordering relation known as dispersion ordering. Further, some conditions are identified under which variance and entropy order similarly when continuous variables are transformed. We also analyze parametric changes which do not disturb the agreement between these rankings. The results are conveniently tabulated in terms of distribution parameters.     

土地价值与城市增长

文章介绍了城市经济动态模型。通过利用在经济学中广泛的效用函数及对效用函数的优化 ,得出城市土地地租有三部份构成 :农业土地地租 ;土地发展成本的租金 ;和区位或可达性所带来的级差地租 ,并进一步推出城市土地价值有四部分构成 :(1)农业土地价值 ;(2 )土地发展成本 ;(3)可达性的经济价值 ;(4)可预见的未来土地地租增值所带来的价值。相对应 ,城市边缘非城市土地价值有两部分组成 :一是与农业土地地租有关的土地价值 ,另一个是可预见的土地转变成城市用地后未来土地地租增值所带来的价值。城市经济动态理论及其结论丰富和发展了土地地租和土地价值理论 ,加深了对土地价值形成和发展的理解 ,有利于相关法规和政策的制定 ,以此提高城市土地利用效益和推动城市发展。最后 ,结合中国国情 ,文章分析了城市政策及土地政策对城市化的社会经济影响。     

卢铿与海尔的价值理念

从首倡“新住宅运动”到践行“新文化地产”，从对“新东方主义”和“新生活方式”的探索与实践到加盟中国顶级民族企业，一位知名企业家的工作变动加速了海尔集团挺进房地产业和构筑海尔地产品牌的进程。10月份，一则消息震动业界：原上海实业发展股份有限公司总裁卢铿受海尔集团总裁张瑞敏之邀，正式加盟海尔集团，出任海尔地产集团的董事长兼首席执行官。