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This paper proposes several methodologies whose objective consists of securing copula density estimates. More specifically, this aim will be achieved by differentiating bivariate least-squares polynomials fitted to Deheuvels' empirical copulas, by making use of Bernstein's approximating polynomials of appropriately selected orders; by differentiating linearized distribution functions evaluated at optimally spaced grid points; and by implementing the kernel density estimation technique in conjunction with a repositioning of the pseudo-observations and a certain criterion for determining suitable bandwidths. Smoother representations of such density estimates can further be secured by approximating them by means of moment-based bivariate polynomials. The various copula density estimation techniques being advocated herein are successfully applied to an actual dataset as well as a random sample generated from a known distribution. [ABSTRACT FROM AUTHOR]

A moment-based density approximation technique that is based on a generalization of Pearson's system of frequency curves is introduced in this paper. More specifically, the derivative of the logarithm of a continuous density function is expressed as a ratio of polynomials whose coefficients are determined by solving a linear system, and a simple representation of the resulting density function is provided. Additionally, a result relating a sample to its moments is stated and derived. It is then explained that, when used in conjunction with sample moments, the methodology being herein advocated can be utilized for the purpose of modeling data sets, irrespective of their size. Several illustrative examples are presented. [ABSTRACT FROM AUTHOR]

A new generalized extended inverse Gaussian density function involving a confluent hypergeometric function is defined. Closed form representations of a generalized extended inverse Gaussian density function and the corresponding moment generating function are provided in terms of Meijer's G-function. Some other statistical functions which are associated with the proposed distribution are also derived. Many distributions can be obtained as limiting cases of the proposed density function. This density is utilized to model an actual data set. The new distribution provides a better fit than related distributions as measured by the Anderson-Darling and Cramér-von Mises statistics. The proposed distribution could, for instance, find applications in the physical and biological sciences and in particular be helpful to researchers working in special functions as well as reliability analysis, survival models and diffraction theory. [ABSTRACT FROM AUTHOR]

moment-based methodology is proposed for approximating the distribution of the distance between two random points belonging to sets that are composed of rectangles. The resulting density approximants are expressed in terms of polynomially adjusted beta density functions. Two norms are being considered: the L¹ norm referred to as the Manhattan distance and the L² norm which corresponds to the Euclidean distance. A few illustrative examples will be presented and certain applications to transportation and routing problems will be pointed out. [ABSTRACT FROM AUTHOR]

Peña and Rodríguez (2002) introduced a portmanteau test for time series which turns out to be more powerful than those proposed by Ljung and Box (1986) and Monti (1994), and approximated its distribution by means of a two-parameter gamma random variable. A polynomially adjusted beta approximation is proposed in this paper. This approximant is based on the moments of the statistic, which can be estimated by simulation or determined by symbolic computations or numerical integration. Various types of time series processes such as AR (1) , MA (1) , ARMA (2, 2) are being considered. The proposed approximation turns out to be nearly exact. [ABSTRACT FROM AUTHOR]

This article proposes a five-parameter exponential-type distribution whose exact moments and normalizing constant are obtained as inverse Mellin transforms and expressed as generalized hypergeometric functions. Several commonly used statistical distributions such as the gamma, Weibull and half-normal turn out to be particular cases of this generalized distribution. It is shown in a numerical example that the proposed distribution produces a better fit than the Weibull or inverse Gaussian distributions when used for modeling a data set consisting of maximum flood levels over a certain time period. [ABSTRACT FROM AUTHOR]

Numerous types of asymmetrical distributions such as the logistic, Weibull, gamma, and beta distributions have been used for modeling various random phenomena such as those encountered in data engineering, pattern recognition, and reliability assessment studies. Several generalizations of the logistic distribution, and certain related models, are proposed in this paper. The corresponding density functions involve an additional parameter, denoted by q, which allows for increased flexibility for modeling purposes; in fact, the larger this parameter is, the lower the mode of the resulting distribution will be. Generalizations of the type-1 and type-2 beta distributions are introduced, along with their logistic-type counterparts; the moments and cumulants of the latter are also derived. Other extensions are discussed including a q-analog of the generalized type-2 beta model, a q-extended generalized logistic distribution, and q-analogs of generalizations of the Dirichlet distribution. As is shown graphically, the proposed univariate distributions can generate a wide array of unimodal or symmetric bimodal curves. [ABSTRACT FROM AUTHOR]

Les auteurs déduisent d'un résultat de Imhof une représentation intégrate de la fonction de répartition d'une combinaison Iinéaire quelconque des composantes d'un vecteur aléatoire de Dirichlet. Comme IIs le font valoir, les lois de plusieurs statistiques peuvent ětre déterminées de façon similaire, notamment celles des rapports du type F, des indices de Moran et de Geary, de la statistique de corrélation spatiale de Cliff-Ord, ou des coefficients de détermination et de corrélation sérielle expérimentaux. Les auteurs expliquent en outre le rǒle clef joué par les combinaisons linéaires des composantes d'un vecteur aléatoire de Dirichlet dans la décomposition de formes quadratiques construites à partir de vecteurs obèissant à une loi sphèrique. IIs déterminent, à titre illustratif, la loi du spectre échantillonnal associé à une chronique générée par un processus de type ARMA. [ABSTRACT FROM AUTHOR]