Related papers: Estimating statistical distributions using an inte…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
In meta-analysis with continuous outcomes, the use of effect sizes based on the means is the most common. It is often found, however, that only the quantile summary measures are reported in some studies, and in certain scenarios, a…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
The full width at half maximum (FWHM) is a useful quantity for characterizing the bandwidth of unimodal functions. However, a closed-form expression for the FWHM of gamma-shaped functions-i.e. functions that are shaped like the gamma…
As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
Using hydrodynamical simulations, we explore the use of the mean and percentiles of the curvature distribution function to recover the equation of state of the high-$z$ ($2 < z < 4$) intergalactic medium (IGM). We find that the mean and…
We investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \rightarrow \mathbb{R}_+$, where $D \subseteq \mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the…
In the present paper we show how obtain the energy distribution f(E) in our vicinity starting from WIMP density profiles in a self consistent way by employing the Eddington approach and adding reasonable angular momentum dependent terms in…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
There is a growing need for flexible statistical distributions that can accurately model data defined on the unit interval. This paper introduces a new unit distribution, termed the unit Shiha (USh) distribution, which is derived from the…
In this paper a method of obtaining smooth analytical estimates of probability densities, radial distribution functions and potentials of mean force from sampled data in a statistically controlled fashion is presented. The approach is…
Distribution-free prediction sets play a pivotal role in uncertainty quantification for complex statistical models. Their validity hinges on reliable calibration data, which may not be readily available as real-world environments often…
The exact expression is derived for the expected value, $< {p_i}> $, for the parameter for any bin $i$ of a histogram following a multinomial distribution derived by sorting $N$ observations into bins of $B$ classes, if $n_i$ of the…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
A fundamental functional in nonparametric statistics is the Mann-Whitney functional ${\theta} = P (X < Y )$ , which constitutes the basis for the most popular nonparametric procedures. The functional ${\theta}$ measures a location or…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of…