The gamma-Lomax distribution

For any continuous baseline G distribution, Zografos and Balakrishnan [On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362] proposed a generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous distribution called the gamma-Lomax distribution, which extends the Lomax distribution is proposed and studied. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The estimation of the model parameters is performed by maximum likelihood. We also determine the observed information matrix. An application illustrates the usefulness of the proposed model.     

Periodic integer-valued GARCH(1, 1) model

This article deals with some probabilistic and statistical properties of a periodic integer-valued GARCH(1,1) model. Necessary and sufficient conditions for the periodical stationary, both in mean and second order, are established. The closed-forms of the mean and the second moment are, under these conditions, obtained. The condition of the existence of higher moment orders and their explicit formula in terms of the parameters are established. The autocovariance structure is studied, while providing the closed-form of the periodic autocorrelation function. The Yule–Walker and the likelihood estimations of the underlying parameters are obtained. A simulation study and an application on real dataset are provided.     

Characterization of a class cf discrete distributions by properties of their moment distributions

The concept of a moment distribution is here applied to the class of factorial series distributions introduced by the author (197U). Moment distributions turn out to have a simple interpretation in this case and often take on a simple form. A few examples are given to illustrate this fact     

Moments of a ratio of two quadratic forms

In this paper, we give the exact moments of a ratio of qua- dratic forms in normal variables, where the quadratic forms are not assumed to be independent. This problem was tackled by other authors who gave approximations and partial results. Here we will give the exact moments for the general case.     

Convergence of the moment generating function of standardized quantiles

A sequence of independent, identically distributed random variables is considered. Given a simple local condition on the distribution of these random variables, we give necessary and sufficient conditions on the tails of the distribution for the moment generating function of a standardized quantile of the first n observations to converge to the moment generating function of an appropriate normal distribution as n →infinity;. This result is actually a special case of a more general result which can also be used to show convergence in distribution and convergence of moments of standardized quantiles.     

Characterizations of Distributions Based on Moments of Residual Life

Let T be a random variable having an absolutely continuous distribution function. It is known that linearity of E(T | T > t) can be used to characterize distributions such as exponential, power and Pareto distribution. In this work, we will extend the above results. More precisely, we characterize the distribution of T by using certain relationships of conditional moments of T. Our results can also be used to obtain new characterization of distributions based on adjacent order statistics or record values.     

New representations of the noncentral chi-square density and cumulative

Representations of noncentral chi-square cumulative distribution function and probability density function are reviewed and new repre¬sentations are given. One representation of the cdf in terms of an integral is easily computed on any machine which has an accurate algorithm for computing the normal cdf.     

基于时变高阶矩模型的贵金属市场风险测度研究

以黄金为代表的贵金属及其金融衍生品的交易量不断增长,逐渐成为与股票和债券平行的投资和避险工具,但关于贵金属市场风险测度的研究却比较缺乏.以上海和伦敦市场的黄金和白银交易价格为样本,基于常数高阶矩模型和时变高阶矩模型建立风险测度模型,计算出不同模型的风险价值和预期损失;采用严谨的后验分析方法,在多头和空头两种头寸共10种分位数水平下对不同模型的风险测度精确性进行后验分析.研究结果表明,在测度风险价值时,时变高阶矩模型的风险测度精确性略优于常数高阶矩模型,带有杠杠效应的时变高阶矩模型优于不带杠杆效应的时变高阶矩模型;综合对比分析不同风险测度模型的后验分析结果可知,对于准确测度贵金属市场的风险,GJR-GARCHSK模型是一个相对合理的选择.     

Bounds of moment generating functions of some life distributions

In this article we show that if a life has new better than used in expectation (NBUE) ageing property and if the mean life is finite then the moment generating function exists and is finite. In fact, the moment generating function is shown to be bounded above by that of the exponential distribution with the same mean. Analogous results are also proven for two much bigger families of life distribution, namely, the new better than renewal used in expectation (NBRUE) and the renewal new is better than used in expectation (RNBUE) and the renewal new better than renewal used in expectation (RNBRUE), provided that the life has finite two moments. Further, stronger results are also obtained for the smaller new better than used version of the above classes.     

均匀磁场中的平面载流线圈

本文以最普遍的方式讨论了任意形状的平面载流圈在均匀磁场中的力学性质，从而在普遍的意义上定义了平面载流圈的磁矩．