A curious integral.
A model for proportions with medical applications
Data that are proportions arise most frequently in biomedical research. In this paper, the exact distributions of R = X + Y and W = X/(X+Y) and the corresponding moment properties are derived when X and Y are proportions and arise from the most flexible bivariate beta distribution known to date. The associated estimation procedures are developed. Finally, two medical data sets are used to illustrate possible applications.
A multimodal beta distribution with application to economic data
Beta distributions are popular models for economic data. In this paper, a new multimodal beta distribution with bathtub shaped failure rate function is introduced. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to consumer price indices...
A series transformation formula and related polynomials.
A truncated bivariate Cauchy distribution.
An Application for the Chebyshev Polynomials
Drought models based on Burr XII variables
Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.
ERRATA: Inequalities associating hypergeometric functions with planar harmonic mappings.
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
Exact and approximate distributions for the product of Dirichlet components
It is well known that has the beta distribution when and follow the Dirichlet distribution. Linear combinations of the form have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose...
Factorial study of a certain parametric distribution.
The general theory of factorial analysis of continuous correspondance (FACC) is used to investigate the binary case of a continuous probability measure defined as:T(x,y) = ayn + b, (x,y) ∈ D & n ∈ N = 0, elsewhereWhere n ≥ 0, a and b are the parameters of this distribution, while the domain D is a variable trapezoidal inscribed in the unit square. The trapezoid depends on two parameters α and β.This problem is solved. As special cases of our problem we obtain a complete solution for...
Factorization of the hypergeometric-type difference equation on the uniform lattice.
Generalized coherent states for oscillators connected with Meixner and Meixner-Pollaczek polynomials.
Hilbert series of the Grassmannian and -Narayana numbers
We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the -Hilbert series is a Vandermonde-like determinant. We show that the -polynomial of the Grassmannian coincides with the -Narayana polynomial. A simplified formula for the -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the -Narayana numbers, i.e. the -polynomial...
Inequalities associating hypergeometric functions with planar harmonic mappings.
Information Matrix for Beta Distributions
2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.
Integral representation of the solutions to Heun's biconfluent equation.
Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions
We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.
Moments of the product distribution.
Muliere and Scarsini's bivariate Pareto distribution: sums, products and ratios.
We derive the exact distributions of R = X + Y, P = X Y and W = X / (X + Y) and the corresponding moment properties when X and Y follow Muliere and Scarsini's bivariate Pareto distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables -obtained using intensive computer power- will be of use to the practitioners of the bivariate Pareto distribution.