Related papers: A quantile-based probabilistic mean value theorem
Building on the notion of $q$-integral introduced by Thomae in 1869, we introduce $q$-order statistics (that, is $q$-analogues of the classical order statistics, for $0<q<1$) which arise from dependent and not identically distributed…
We propose a novel framework for modeling the yield curve from a quantile perspective. Building on the dynamic Nelson-Siegel model of Diebold et al. (2006), we extend its traditional mean-based approach to a quantile regression setting,…
A new class of stochastic variables, governed by a specifice set of rules, is introduced. These rules force them to loose some properties usually assumed for this kind of variables. We demonstrate that stochastic processes driven by these…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…
In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Some properties of the inverse of the Normal distribution are studied. Its derivatives, integrals and asymptotic behavior are presented.
This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to…
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…
Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions.…
From the perspective of expectations of randomly stopped sums, Wald's equation and the Optional Sampling Theorem identify situations in which the stopping time can be decoupled from the stopping place, acting as if the two were independent.…
We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We investigate the probability equivalent level of Value at Risk and $n^{\mathrm{th}}$-order Expected Shortfall (called PELVE_n), which can be considered as a variant of the notion of the probability equivalent level of Value at Risk and…
Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…