A curious integral.
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Masson, David R. (1996)
International Journal of Mathematics and Mathematical Sciences
Saralees Nadarajah (2007)
Applicationes Mathematicae
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.
Saralees Nadarajah, Samuel Kotz (2007)
Applicationes Mathematicae
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...
Boyadzhiev, Khristo N. (2005)
International Journal of Mathematics and Mathematical Sciences
Nadarajah, Saralees, Kotz, Samuel (2007)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
Đurđe Cvijović, Jacek Klinowski (1998)
Matematički Vesnik
Saralees Nadarajah, B. M. Golam Kibria (2006)
Applicationes Mathematicae
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.
Ahuja, Om P., Silverman, Herb (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Corinne Berzin, José R. León (2008)
Annales de l'I.H.P. Probabilités et statistiques
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(⋅)...
Saralees Nadarajah, Samuel Kotz (2004)
Kybernetika
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...
A. Y. Yehia, K. I. Hamouda, Assem A. Tharwat (1991)
Trabajos de Estadística
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...
Álvarez-Nodarse, R., Atakishiyev, N.M., Costas-Santos, R.S. (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Borzov, V.V., Damaskinskiĭ, E.V. (2004)
Zapiski Nauchnykh Seminarov POMI
Lukas Braun (2019)
Communications in Mathematics
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...
Ahuja, Om P., Silverman, H. (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Aryal, Gokarna, Nadarajah, Saralees (2004)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.
Belmehdi, S., Chehab, J.-P. (2004)
Abstract and Applied Analysis
Sadhana Mishra (1991)
Annales Polonici Mathematici
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.
Nadarajah, Saralees, Kotz, Samuel (2006)
Applied Mathematics E-Notes [electronic only]
Saralees Nadarajah, Samuel Kotz (2005)
SORT
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.
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