arXiv subjects

Omar Eidous

Publications and source records attributed to Omar Eidous.

5 recordsLinked to original sources

arXiv2026

Beyond Pairwise: Nonparametric Kernel Estimators for a Generalized Weitzman Coefficient Across k Distributions

This papers presents a generalization of the Weitzman overlapping coefficient, originally defined for two probability density functions, to a setting involving k independent distributions, denoted by Delta. To estimate this generalized coefficient, we develop nonparametric methods based on kernel density estimation using k independent random samples (k>=2). Given the analytical complexity of directly deriving Delta using kernel estimators, a novel estimation strategy is proposed. It reformulates Delta as the expected value of a suitably defined function, which is then estimated via the method of moments and the resulting expressions are combined with kernel density estimators to construct the proposed estimators. This method yields multiple new estimators for the generalized Weitzman coefficient. Their performance is evaluated and compared through extensive Monte Carlo simulations. The results demonstrate that the proposed estimators are both effective and practically applicable, providing flexible tools for measuring overlap among multiple distributions.

stat.ME↗

arXiv2026

A Simpson Based Estimation Approach for the Overlapping Coefficient of k>=2 Normal Distributions

The overlapping coefficient is a fundamental measure of similarity between probability distributions. While the case of two distributions has been extensively studied, extending this measure to multiple populations presents both analytical and computational challenges. In this paper, we propose a general estimation framework for the overlapping coefficient of k>=2 normal distributions. The method employs Simpsons numerical integration rule combined with plug-in maximum likelihood estimators of the normal parameters. The resulting estimator is shown to be consistent under standard regularity conditions. A Monte Carlo simulation study is conducted across various overlap scenarios and sample sizes. The results demonstrate that the proposed Simpson based estimator performs competitively for all overlap levels, with notable advantages in low overlap situations. This methodology offers a flexible and computationally efficient approach applicable to an arbitrary number of normal populations.

stat.ME↗

arXiv2024

On Inference of Weitzman Overlapping Coefficient in Two Weibull Distributions

Studying overlapping coefficients has recently become of great benefit, especially after its use in goodness-of-fit tests. These coefficients are defined as the amount of similarity between two statistical distributions. This research examines the estimation of one of these overlapping coefficients, which is the Weitzman coefficient Δ, assuming two Weibull distributions and without using any restrictions on the parameters of these distributions. We studied the relative bias and relative mean square error of the resulting estimator by implementing a simulation study. The results show the importance of the resulting estimator.

stat.ME↗

arXiv2022

Estimation of Matusita Overlapping Coefficient for Pair Normal Distributions

The Matusita overlapping coefficient is defined as agreement or similarity between two or more distributions. The parametric normal distribution is one of the most important statistical distributions. Under the assumption that the data at hand follow two independent normal distributions, this paper suggests a new technique to estimate the Matusita coefficient. In contrast to the studies in the literature, the suggested technique requires no assumptions on the location and scale parameters of the normal distributions. The finite properties of the resulting estimators are investigated and compared with the nonparametric kernel estimators and with some existing estimators via simulation techniques. The results show that the performance of the proposed estimators is better than the kernel estimators for all considered cases.

stat.ME↗

arXiv2022

Improvements of Polya Upper Bound for Cumulative Standard Normal Distribution and Related Functions

Although there is an extensive literature on the upper bound for cumulative standard normal distribution, there are relatively not sharp for all values of the interested argument x. The aim of this paper is to establish a sharp upper bound for standard normal distribution function, in the sense that its maximum absolute difference from phi(x) is less than for all values of x. The established bound improves the well-known Polya upper bound and it can be used as an approximation for Phi(x) itself with a very satisfactory accuracy. Numerical comparisons between the proposed upper bound and some other existing upper bounds have been achieved, which show that the proposed bound is tighter than alternative bounds found in the literature.

stat.CO↗