arXiv subjects

Elsayed A. H. Elamir

Publications and source records attributed to Elsayed A. H. Elamir.

4 recordsLinked to original sources

arXiv2025

The Role of Mean Absolute Deviation Function in Obtaining Smooth Estimation for Distribution and Density Functions: Beta Regression Approach

Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a simple approach but novel for estimating both functions via beta regression and generalized additive model approaches. The approach explores estimation of both functions by smoothing the first derivative of left mean absolute deviation function to obtain the final optimal smooth estimates under the condition of nondecreasing distribution function, and the density function remains nonnegative. This is achieved by using beta regression and generalized additive model with various link functions (logit, probit, cloglog, and cauchit) that applied to a polynomial function whose degree is determined by less mean absolute regression errors. Additionally, confidence limits for the distribution function are derived based on the beta distribution to give judgement about precision of obtained estimates. The method is utilized on simulated datasets featuring unimodal and multimodal and an actual dataset. The results suggest that this method exhibits strong performance relative to the kernel-based method, especially for its superior attributes in sample sizes and smoothness.

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arXiv2022

On Uses of Mean Absolute Deviation: Shape Exploring and Distribution Function Estimation

Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an important fundament for successful data analytic. Furthermore, new nonparametric approaches for estimating the cumulative distribution function based on the mean absolute deviation function are proposed. These new approaches are meant to be a general nonparametric class that includes the empirical distribution function as a special case. Simulation study reveals that the Richardson extrapolation approach has a major improvement in terms of average squared errors over the classical empirical estimators and has comparable results with smooth approaches such as cubic spline and constrained linear spline for practically small samples. The properties of the proposed estimators are studied. Moreover, the Richardson approach applied for real data application and used to estimate the hazardous concentration five percent.

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arXiv2022

A Graphical Approach for Friedman Test: Moments Approach

Friedman test is a nonparametric method that proposed for analyzing data from a randomized complete block design as a robust alternative to parametric method and widely applied in many fields such as agriculture, biology, business, education, and medicine. After the null hypothesis of no treatment effects is rejected, the post-hoc pairwise comparisons must be applied to identify where the differences occur. As the number of groups increases, the number of required comparisons becomes large and this may increase the type I error. The aim of this study is twofold. The main aim is to suggest expression that facilitates the plotting Friedman test by gathering the test and pairwise comparisons in one simple step. The second aim is to derive the sampling distribution of the suggested expression by utilizing method of moments that helps in obtaining the decision limit. An application and simulation study are carried out to show the advantage of the suggested method and to compute the empirical type I error. The results are of great value where the proposed method makes huge reduction in the number of required tests to show where the discrepancies occur, holds the type I error close to the nominal value and provides visual, deep insight and understanding where the treatment effects occur.

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arXiv2020

Simultaneous test for Means: An Unblind Way to the F-test in One-way Analysis of Variance

After rejecting the null hypothesis in the analysis of variance, the next step is to make the pairwise comparisons to find out differences in means. The purpose of this paper is threefold. The foremost aim is to suggest expression for calculating decision limit that enables us to collect the test and pairwise comparisons in one step. This expression is proposed as the ratio of between square for each treatment and within sum of squares for all treatments. The second aim is to obtain the exact sampling distribution of the proposed ratio under the null hypothesis. The exact sampling distribution is derived as the beta distribution of the second type. The third aim is to use beta distribution and adjusted p values to create decision limit. Therefore, reject the null hypothesis of equal means if any adjusted point falls outsides the decision limit. Simulation study is conducted to compute Type one error. The results show that the proposed method controls the type one error near nominal values using Benjamini-Hochberg adjusted p-values. Two applications are given to show the benefits of the proposed method.

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