Related papers: On the Unit Teissier Distribution: Properties, Est…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
Up-and-Down (U&D) is a popular sequential design for estimating threshold percentiles in binary experiments. However, U&D application practices have stagnated, and significant gaps in understanding its properties persist. The first part of…
U-max statistics were introduced by Lao and Mayer in 2008. Instead of averaging the kernel over all possible subsets of the original sample, they considered the maximum of the kernel. Such statistics are natural in stochastic geometry.…
We consider the question of estimating multi-dimensional Gaussian mixtures (GM) with compactly supported or subgaussian mixing distributions. Minimax estimation rate for this class (under Hellinger, TV and KL divergences) is a long-standing…
With some regularity conditions maximum likelihood estimators (MLEs) always produce asymptotically optimal (in the sense of consistency, efficiency, sufficiency, and unbiasedness) estimators. But in general, the MLEs lead to non-robust…
A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…
A new 2 parameter unit Weibull distribution is defined on the unit interval (0,1). The methodology of deducing its PDF, some of its properties and related functions are discussed. The paper is supplied by many figures illustrating the new…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati (2016). This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as…
We introduce the \textsc{Tailed-Uniform} proposal distribution for generating training simulations in simulation-based inference. Instead of sampling parameters uniformly within bounded regions, we extend the distribution beyond prior…
The Yule-Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule-Simon…
The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…
This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
The increasing deployment of distribution-level phasor measurement units (PMUs) calls for dynamic distribution state estimation (DDSE) approaches that tap into high-rate measurements to maintain a comprehensive view of the…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
We develop a new approach for estimating the expected values of nonlinear functions applied to multivariate random variables with arbitrary distributions. Rather than assuming a particular distribution, we assume that we are only given the…