Related papers: Solution for the Indefinite Integral of the Standa…
The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
We derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form…
We define the notion of distribution on an infinite dimensional space motivated by the notion of Feynman path integral and by construction of probability measures for generalized random fields. This notion of distribution turns out to be…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
Let $X^{(\mu)}(ds)$ be an $\mathbb{R}^d$-valued homogeneous independently scattered random measure over $\mathbb{R}$ having $\mu$ as the distribution of $X^{(\mu)}((t,t+1])$. Let $f(s)$ be a nonrandom measurable function on an open interval…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
We consider a multivariate density model where we estimate the excess mass of the unknown probability density $f$ at a given level $\nu>0$ from $n$ i.i.d. observed random variables. This problem has several applications such as…
We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…