Algorithm for Finding the Proper Continuous Distribution Function to a Unimodal Empirical Distribution Function

Abstract

We present an algorithm containing the first step towards solving one of the Fundamental Problems of Non-parametric Mathematical Statistics: determining the distribution of an unknown unimodal continuous population from which we have a large random sample of discrete observations. We will present the “algorithm of non-fitting” with the help of which, by using the so-called relative increment functions as auxiliary functions, one can eliminate a large class of classical continuous unimodal distributions which our population does not belong to. In the remaining class of unimodal and smooth distributions one can approximate the distribution of the population in question. The algorithm is illustrated in three numerical examples.

A Study of Conflict Issues Affecting Ugandan Housemaids who Migrate to Saudi Arabia and How to Mitigate them

March 10, 2026

This study aims to comprehensively analyse the complex interplay between