On the generalized Poisson distribution

We use Euler's difference lemma to prove that, for θ > 0 and 0 ≤λ < 1, the function P _n defined on the non-negative integers by
P _n (θ, λ) = [θ(θ + n λ) ^{n −1}/ n !]e^{− n λ−θ}
defines a probability distribution, known as the Generalized Poisson Distribution.     

Autocovariance functions of series and of their transforms

We derive a method to link exactly the autocovariance functions of two arbitrary instantaneous transformations of a time series. For example, this is useful when one wants to derive the autocovariance of the logarithm of a series from the known autocovariance of the original series and, more generally, when one wishes to describe the time-series effects of applying a nonlinear transformation to a process whose properties are known. As an illustration, we provide two corollaries and three examples. The first corollary is on the commonly used logarithmic transformation, and is applied to a geometric auto-regressive (AR) process, as well as to a positive moving-average (MA) process. The second corollary is on the tan⁻¹(·) transformation which will turn possibly unstable series into stable ones. As an illustration, we obtain the autocovariance function of the tan⁻¹(·) of an arithmetic AR process. This filter, while always producing a bounded process, preserves the stability/instability distinction of the original series, a feature that can be turned to an advantage in the design of tests. We then present a probabilistic interpretation of the main features of the new autocovariance function. We also provide a mathematical lemma on a general integral which is of independent interest.     

Order preserving functions and generalized convexity

In order to better understand the monotonicity properties which characterize the gradient of pseudoconvex and quasi convex funzions, psedomonotonicity and quasi monotonicity can be introduced. A quite different approach is proposed in this paper, by defining new order relations, whose preservation leads precisely to several kinds of pseudoconvexity and quasi convexity. Some general properties of order preservation are proved; they are useful to state necessary and sufficient conditions of monotonicity for particular orders related with generalized convexity.     

Nonparametric estimation of distribution functions

Summary Using Silverman and Young’s (1987) idea of rescaling a rescaled smoothed empirical distribution function is defined and investigated when the smoothing parameter depends on the data. The rescaled smoothed estimator is shown to be often better than the commonly used ordinary smoothed estimator.     

A new bivariate generalized Poisson distribution

In this paper, a new bivariate generalized Poisson distribution (GPD) that allows any type of correlation is defined and studied. The marginal distributions of the bivariate model are the univariate GPDs. The parameters of the bivariate distribution are estimated by using the moment and maximum likelihood methods. Some test statistics are discussed and one numerical data set is used to illustrate the applications of the bivariate model.     

提升配送功能的思考

通过对配送路线的设计与修改，配送方式的选择与变化，配送工具的使用与管理、配送人员的安排和变化等几个方面进行了具体的阐述与探讨，以利进一步提升物流配送的能力。     

Bivariate generalized Poisson distribution with some applications

The univariate generalized Poisson probability model has many applications in various areas such as engineering, manufacturing, survival analysis, genetic, shunting accidents, queuing, and branching processes. A correlated bivariate version of the univariate generalized Poisson distribution is defined and studied. Estimation of its parameters and some of its properties are also discussed.     

An extremal property of the generalized arcsine distribution

The main result of the paper is the following characterization of the generalized arcsine density p _γ (t) = t ^γ?1(1 ? t) ^γ?1/B(γ, γ)   with ${t \in (0, 1)}$ and ${\gamma \in(0,\frac12) \cup (\frac12,1)}$ : a r.v. ξ supported on [0, 1] has the generalized arcsine density p _γ (t) if and only if ${ {\mathbb E} |\xi- x|^{1-2 \gamma}}$ has the same value for almost all ${x \in (0,1)}$ . Moreover, the measure with density p _γ (t) is a unique minimizer (in the space of all probability measures μ supported on (0, 1)) of the double expectation ${ (\gamma-\frac12 ) {\mathbb E} |\xi-\xi^{\prime}|^{1-2 \gamma}}$ , where ξ and ξ′ are independent random variables distributed according to the measure μ. These results extend recent results characterizing the standard arcsine density (the case ${\gamma=\frac12}$ ).     

A generalized maximum likelihood characterization of the normal distribution

LetP be a probability measure on ℝ andI _x be the set of alln-dimensional rectangles containingx. If for allx ∈ ℝⁿ and θ ∈ ℝ the inequality holds,P is a normal distributioin with mean 0 or the unit mass at 0. The result generalizes Teicher’s (1961) maximum likelihood characterization of the normal density to a characterization ofN(0, σ²) amongall distributions (including those without density). The m.l. principle used is that of Scholz (1980).     

Nonparametric Bayes inference for concave distribution functions

Bayesian inference for concave distribution functions is investigated. This is made by transforming a mixture of Dirichlet processes on the space of distribution functions to the space of concave distribution functions. We give a method for sampling from the posterior distribution using a Pólya urn scheme in combination with a Markov chain Monte Carlo algorithm. The methods are extended to estimation of concave distribution functions for incompletely observed data.     

Record values from generalized Pareto distribution and associated inference

In this paper, we derive exact explicit expressions for the single, double, triple and quadruple moments of the upper record values from a generalized Pareto distribution. We then use these expressions to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of record values. Finally, we develop approximate confidence intervals for the location and scale parameters of the generalized Pareto distribution using the Edgeworth approximation and compare them with the intervals constructed through Monte Carlo simulations. Received: June 1999     

On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

On intermediate utility functions

Intermediate utility functions have been recently introduced by Persson and Tabellini (2000, Political Economics: Explaining Economics Policy, MIT Press, Cambridge) and ensure the existence of a majority voting equilibrium at multi-dimensional voting. Here, we show that monotone transforms of these utility functions also are sufficient for the existence of a Condorcet winner.     

Numerical distribution functions of likelihood ratio tests for cointegration

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith ( 1997 ) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously. The principal contributions of the paper are a set of data files that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them. This program, which is freely available via the Internet, can be used to calculate both asymptotic critical values and P-values. Copyright © 1999 John Wiley & Sons, Ltd.     

A note on a short table of the generalized hypergeometric distribution

In a paper byMathai/Saxena [1968, 21–39], the present authors found some entries with error and others with lack of precision. Recently,Conde/Kalla [1979] have tabulated₂ F ₁ (a, b; c; x) fora=0.5 (0.5) 5.0,b=0.5 (0.5) 5.0,c=0.5 (0.5) 12 andx=–2.50 (0.05) 0.95. The present note explains the method of computation and checks applied, Wronskians, continuation formulae, special cases etc. to insure the stated accuracy.