Elliptical symmetry and exchangeability with characterizations

AbstractWe establish certain general characterization results on elliptically symmetric distributions and exchangeable random variables. These results yield, in particular, the results given earlier by Maxwell, Bartlett, Kingman, Ali, Smith, Arnold and Lynch, and several others

A Trinomial Difference Distribution

A trinomial difference distribution is defined and its distributional properties are illustrated. This distribution present the binomial difference distribution as a special case. The moment estimators and maximum likelihood estimators of the trinomial difference distribution are compared via simulation study. Two applications are modeled with the trinomial difference distribution and compared with other possible distributions.Una distribución de diferencia trinomial se define en este artículo así como sus propiedades distribucionales. Esta distribución cuenta con la distribución de diferencia binomial como un caso particular. Los estimadores de momentos y de máxima verosimilitud son comparados vía un estudio de simulación. Dos aplicaciones son modelados con la distribución diferencia trinomial y se comparan con otras distribuciones posibles

A Bivariate Model based on Compound Negative Binomial Distribution

A new bivariate model is introduced by compounding negative binomial and geometric distributions. Distributional properties, including joint, marginal and conditional distributions are discussed. Expressions for the product moments, covariance and correlation coefficient are obtained. Some properties such as ordering, unimodality, monotonicity and self-decomposability are studied. Parameter estimators using the method of moments and maximum likelihood are derived. Applications to traffic accidents data are illustrated.Un nuevo modelo de dos variables se introduce mediante la composición distribuciones binomiales negativos y geométricos. propiedades distributivas, incluyendo distribuciones conjuntas, marginales y condicionales se discuten. se obtienen las expresiones para los momentos de productos, la covarianza y el coeficiente de correlación. Se estudian algunas propiedades tales como pedidos, unimodalidad, monotonía y la auto-decomposability. estimadores de parámetros utilizando el método de los momentos y de máxima verosimilitud se derivan. Aplicaciones a los datos de accidentes de tráfico se ilustra

Uniformly Shifted Exponential Distribution

The use of life distributions has increased over the past decade, receiving particular attention in recent years, both from a practical and theoretical point of view. Life distributions can be used in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. This paper presents and investigates a new life distribution. The proposed model shows favorable characteristics in terms of reliability theory, which makes it competitive against other commonly used life distributions, such as the exponential, gamma, and Weibull distributions. The methods of maximum likelihood and moments are used to estimate the parameters of the proposed model. Additionally, real-life data drawn from different fields are used to illustrate the usefulness of the new distribution. Further, the R programming language is used to perform all computations and produce all graphs

Dispersivity and stochastic majorization

Inequalities and monotonicity results are obtained for order statistics from distributions ordered by dispersivity. One results solves the open problem posed by Marshall and Olkin (1979, p. 282). Applications of these results are given.Dispersive ordering majorization Schur functions stochastic ordering variability ordering order statistics dispersive function stochastic majorization

On the generalized Euler distribution

In this paper, a new family of distributions is introduced which we name the generalized Euler distributions. This family arises as a consequence of investigating optimal strategies for drilling in an oil exploration model. Properties of this family are presented.Euler distribution oil exploration

On bivariate Poisson regression models

In this paper, we consider estimating the parameters of bivariate and zero-inflated bivariate Poisson regression models using the conditional method. This method is compared with the standard method, which uses the joint probability function. Simulations and real applications show that the two methods have almost identical Akaike Information Criteria and parameter estimates, but the conditional method has a much faster execution time than the joint method. We conducted our computations using the R and SAS package. Our results also indicate that the execution time of SAS is faster than that of R

Elliptical symmetry and exchangeability with characterizations

We establish certain general characterization results on elliptically symmetric distributions and exchangeable random variables. These results yield, in particular, the results given earlier by Maxwell, Bartlett, Kingman, Ali, Smith, Arnold and Lynch, and several others.elliptically and spherically symmetric distributions exchangeable random variables de Finetti's theorem Skitovic-Darmois theorem Schoenberg representation for spherical distributions

Solution of the integrated Cauchy functional equation a half line using on exchangeability

A new proof is given based on an infinite sequence of exchangeable random variables for the solution of the integrated Cauchy functional equation studied by Lau and Rao (1982)

An application of the Perron-Frobenius theorem to a Damage Model Problem

Using the Perron-Frobenius theorem, it is established that if (X, Y) is a random vector of non-negative integer-valued components such that Y≤X almost surely and two modified Rao-Rubin conditions hold, then under some mild assumptions the distribution of (X, Y) is uniquely determined by the conditional distribution of Y given X. this result extends the recent unpublished work of Shanbag and Taillie (1979) on damage models