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This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a…
This paper studies the problem of {\em learning} the probability distribution $P_X$ of a discrete random variable $X$ using indirect and sequential samples. At each time step, we choose one of the possible $K$ functions, $g_1, \ldots, g_K$…
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions. Focusing on the case of strong-convex and smooth potentials, in this paper, we…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, 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…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
The Birnbaum-Saunders distribution is a flexible and useful model which has been used in several fields. In this paper, a new bimodal version of this distribution based on the alpha-skew-normal distribution is established. We discuss some…
In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe…
A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator (MLE) is a retraction from that simplex onto the model. We characterize all models for which this retraction is a rational function. This is…
This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular…
The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…