Selecting the Best Regression Equation via the P-Value of F-Test.
Sharp upper bounds for the best predictor of future mean of some order statistics
We provide sharp upper bounds for the mean of the future order statistics based on observed r order statistics. These bounds are expressed in terms of various scale units. We also determine the probability distributions for which the bounds are attained.
Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes.
In this paper we investigate two classes of exponential dispersion models (EDMs) for overdispersed count data with respect to the Poisson distribution. The first is a class of Poisson mixture with positive Tweedie mixing distributions. As an approximation (in terms of unit variance function) of the first, the second is a new class of EDMs characterized by their unit variance functions of the form μ + μp, where p is a real index related to a precise model. These two classes provide some alternatives...
Some methods of estimation for a trivariate Poisson distribution
Some Notes on the Non-central Negative Binomial Distribution.
Some properties and applications of probability distributions based on MacDonald function
In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types and are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications...
Some properties and applications of the stuttering generalized Waring distribution.
Some properties of beta functions and the distribution for the product of independent beta random variables.
Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration,...
Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective
Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler functions are...
Some Properties of the Distribution of an Operational Ridge Estimator.
Some Statistical Problems in the Presence of an Outlier When Sampling from Truncation Parameter Densities.
Statistical aspects of associativity for copulas
In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity...
Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics
Symmetries of random discrete copulas
In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.