On Sampling Designs with Ordered Conditional Inclusion Probabilities

In this paper we consider a family of sampling designs for which increasing first‐order inclusion probabilities imply, in a specific sense, increasing conditional inclusion probabilities. It is proved that the complementary Midzuno, the conditional Poisson, and the Sampford designs belong to this family. It is shown that designs of the family are more efficient than a comparable with‐replacement design. Furthermore, the efficiency gain is explicitly given for these designs.     

Sharp Bounds for Generalized Order Statistics via Logarithmic Moments

ABSTRACT

We present sharp bounds for expectations of generalized order statistics with random indices. The bounds are expressed in terms of logarithmic moments E X ^a (log max {1, X}) ^b of the underlying observation X. They are attainable and provide characterizations of some non trivial distributions. No restrictions are imposed on the parameters of the generalized order statistics model.     

Some Characterizations Based on Entropy of Order Statistics and Record Values

In the literature of information theory, Shannon entropy plays an important role and in the context of reliability theory, order statistics and record values are used for statistical modeling. The aim of this article is characterizing the parent distributions based on Shannon entropy of order statistics and record values. It is shown that the equality of the Shannon information in order statistics or record values can determine uniquely the parent distribution. The exponential distribution is characterized through maximizing Shannon entropy of record values under some constraints. The results are useful in the modeling problems.     

The Beta-Dagum Distribution: Definition and Properties

This article introduces a five-parameter Beta-Dagum distribution from which moments, hazard and entropy, and reliability measures are then derived. These properties show the high flexibility of the said distribution. The maximum likelihood estimators of the Beta-Dagum parameters are examined and the expected Fisher information matrix provided. Next, a simulation study is carried out which shows the good performance of maximum likelihood estimators for finite samples. Finally, the usefulness of the new distribution is illustrated through real data sets.     

The New Zenga curve in the context of reliability analysis

ABSTRACT

In this article, we look into the properties and characterizations of the New Zenga curve. The relationship of the curve with other measures of inequality as well as some reliability concepts are examined. Classification of lifetime distributions using the Zenga curve and an illustration for the behaviour of the curve using a survival data are also provided.     

Simultaneous prediction intervals for regression models with an intercept

Consider the usual linear regression model y = x’β+?, relating a response y to a vector of predictors x. Suppose that n observations on y together with the corresponding values of x are available , and it is desired to construct simultaneous prediction intervals for k future values of y at values of x which can not be ascertained beforehand. In most applications the regression model contains an intercept. This paper presents two sets of prediction intervals appropriate to this case. The proposed intervals are compared with those of Carlstein (1986), and the improvements are illustrated in the case of simple linear regression.     

A method for estimating lorenz curves

This paper proposes a new method for estimating the parameters of Lorenz Curves (LC’s) and fitting LC’s to observed data. The method is very general. It is applicable to any family of LC’s as long as it is given in closed form which is often the case in practice. The method can also be applied to either the LC or to its associated distribution. The estimators are easy to compute as they are obtained one at a time by solving only one equation in one unknown and in many cases the solutions are given in closed-forms. An additional advantage, that is not shared with the currently used method of estimation, is that the method is invariant as to the specification of which variable is written as a function of the other in the LC form. The method is applied to the most commonly suggested LC’s families. An example of real-life data is used to illustrate the methodology. A simulation study is performed to study the properties of the proposed estimators and to compare them with existing ones. The results seem to indicate that the proposed estimators have good properties and they often perform much better than the existing ones.     

收入不平等与经济发展——基于中国省际面板数据的分析

基于1987-2005年的中国省级面板数据对收入不平等与经济发展之间的关系进行了分析.有证据表明中国确实存在着不平等程度随经济发展先提高后降低的现象(也即不平等与经济发展水平存在Kuznets倒U型关系),转折点大约在人均GDP达到15 870元(1987年价格水平)时出现.文章随后分析了收入不平等对经济发展的影响,结果发现本期的经济增长速度随着上期收入不平等水平的提高呈现先升后降的趋势.在收入不平等的变化对经济增长的影响方面没有发现一致的结论.