相关论文: Holonomic gradient method for distribution functio…
In this paper, we consider the problem of estimating the density function of a Chi-squared variable on the basis of observations of another Chi-squared variable and a normal variable under the Kullback-Leibler divergence. We assume that…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach.…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
Starting with a non-abelian gerbe represented by a non-abelian differential cocycle, with values in a given crossed-module, this paper explicitly calculates a formula for the derivative of the associated surface holonomy of squares mapped…
We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves…
This paper proposes a symbolic-numeric Bayesian filtering method for a class of discrete-time nonlinear stochastic systems to achieve high accuracy with a relatively small online computational cost. The proposed method is based on the…
The cumulants and moments of the log of the non-central chi-square distribution are derived. For example, the expected log of a chi-square random variable with v degrees of freedom is log(2) + psi(v/2). Applications to modeling probability…
We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term ${}_1F_1$ in the non-central uni-variate Student's $t$. Some extensions of matrix-variate distributions…
The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
We give the general form for a germ of holonomic distribution of one complex variable.
We introduce a class of logarithmic Lambert W random variables for a specific family of distributions. In particular, we characterize the log-Lambert W random variables for chi-squared distributions which naturally appear in the likelihood…
The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute…
This paper develops a polynomial normal transformation model, whereby various non-normal probability distributions can be simulated by the standard normal distribution. Two methods are presented to determine the coefficients of polynomial…
The ability to estimate joint, conditional and marginal probability distributions over some set of variables is of great utility for many common machine learning tasks. However, estimating these distributions can be challenging,…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
Necessary and sufficient conditions are obtained under which the numerator of the partial derivative of a rational function holomorphic in open upper poly-halfplane is the sum of squares of polynomials.
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…