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Moments of q-Normal and conditional q-Normal distributions  [PDF]
Pawe? J. Szab?owski
Statistics , 2015, DOI: 10.1016/j.spl.2015.06.027
Abstract: We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and Kesten-McKay ($q=0,$ conditional $q-$Normal) distributions. As a by product we get asymptotic properties of some expansions in modified Bessel functions.
Ergodicity and stability of the conditional distributions of nondegenerate Markov chains  [PDF]
Xin Thomson Tong,Ramon van Handel
Mathematics , 2011, DOI: 10.1214/11-AAP800
Abstract: We consider a bivariate stationary Markov chain $(X_n,Y_n)_{n\ge0}$ in a Polish state space, where only the process $(Y_n)_{n\ge0}$ is presumed to be observable. The goal of this paper is to investigate the ergodic theory and stability properties of the measure-valued process $(\Pi_n)_{n\ge0}$, where $\Pi_n$ is the conditional distribution of $X_n$ given $Y_0,...,Y_n$. We show that the ergodic and stability properties of $(\Pi_n)_{n\ge0}$ are inherited from the ergodicity of the unobserved process $(X_n)_{n\ge0}$ provided that the Markov chain $(X_n,Y_n)_{n\ge0}$ is nondegenerate, that is, its transition kernel is equivalent to the product of independent transition kernels. Our main results generalize, subsume and in some cases correct previous results on the ergodic theory of nonlinear filters.
Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law  [PDF]
S. G. Bobkov,G. P. Chistyakov,F. G?tze
Mathematics , 2015,
Abstract: For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.
On Markov processes with polynomials conditional moments  [PDF]
Pawe? J. Szab?owski
Mathematics , 2012,
Abstract: We study properties of a subclass of Markov processes that have all moments that are continuous functions of the time parameter and more importantly are characterized by the property that say their $n-$th conditional moment given the past is also a polynomial of degree not exceeding $n.$ Of course all processes with independent increments with all moments belong to this class. We give characterization of them within the studied class. We indicate other examples of such process. Besides we indicate families of polynomials that have the property of constituting martingales. We also study conditions under which processes from the analysed class have orthogonal polynomial martingales and further are harnesses or quadratic harnesses. We provide examples illustrating developed theory and also provide some interesting open questions. To make paper interesting for a wider range of readers we provide short introduction formulated in the language of measures on the plane.
Conditional Dependence of Trivariate Generalized Pareto Distributions  [PDF]
Diakarya Barro
Asian Journal of Mathematics & Statistics , 2009,
Abstract: In this study we consider the dependence of the family of multivariate generalized Pareto distributions under given conditions on lower dimensional margins. A new function which describes this conditional dependence is built via Pickands dependence function. This function provides a new characterization of the basic subfamilies of trivariate generalized Pareto distributions.
Characterizations of multinomial distributions based on conditional distributions
Khoan T. Dinh,Truc T. Nguyen,Yining Wang
International Journal of Mathematics and Mathematical Sciences , 1996, DOI: 10.1155/s0161171296000828
Abstract: Several characterizations of the joint multinomial distribution of two discrete random vectors are derived assuming conditional multinomial distributions.
On Moments of the Power Series Distributions
Slavko Simic
The Open Statistics & Probability Journal , 2009, DOI: 10.2174/1876527000901010003]
Abstract: For the Power Series Distributions generated by an arbitrary entire function of finite order, applying methods of Karamata’s Theory of Regular Variation, we obtain asymptotic behavior of its moments. As an illustration, we calculate the moments of distributions generated by the class of Mittag-Leffler functions of which the well-known Poisson Law is just a special case.
Identification of Conditional Interventional Distributions  [PDF]
Ilya Shpitser,Judea Pearl
Computer Science , 2012,
Abstract: The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting conditional distributions resulting from performing an action on a set of variables and, subsequently, taking measurements of another set. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem.
Truncated moments of parton distributions  [PDF]
Stefano Forte,Lorenzo Magnea
Physics , 1998, DOI: 10.1016/S0370-2693(99)00065-9
Abstract: We derive evolution equations satisfied by moments of parton distributions when the integration over the Bjorken variable is restricted to a subset (x_0 <= x <= 1) of the allowed kinematical range 0<= x<= 1. The corresponding anomalous dimensions turn out to be given by a triangular matrix which couples the N--th truncated moment with all (N + K)--th truncated moments with integer K >= 0. We show that the series of couplings to higher moments is convergent and can be truncated to low orders while retaining excellent accuracy. We give an example of application to the determination of alpha_s from scaling violations.
A Portfolio Selection Model Conditional on Non-normal Stable Distributions: Mean-scale Parameter Model

XU Xu-song,HOU Cheng-qi,

系统工程理论与实践 , 2006,
Abstract: Because empirical distributions of rates of return on risky securities have characters of skewness and excess kurtosis,this article puts forward studying portfolio selection model conditional on non-normal stable distributions.We find that fitness of returns on stocks to non-normal stable distributions in China stock market is very good by fitness test;study measurements of return and risk of a portfolio conditional on non-normal stable distributions and put forward mean-scale parameter model;find that mean-scale parameter model can explain asset allocation puzzle by empirical analysis.
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