EXCEL-oriented procedures for determining the entropy of a distribution function and its relative parametric sensitivity (elasticity) under the conditions of two-sided restrictions on the range of values of a continuous random variable

Abstract

The goal of the work. Development of an EXCEL-oriented calculator for calculating entropy and its elasticity for distribution functions under the condition of a limited domain of definition of a continuous random variable. Subject of study. Probability density functions and their entropy under the condition of bilateral restrictions on the domain of possible values of random variables. Research methods. Algorithmic and numerical analysis of procedures for obtaining numerical values of entropy of density functions of continuous random variables under the condition of two-way restrictions on the area of its definition. The obtained results. The work proposes an EXCEL-oriented calculator for calculating entropy and its elasticity for distribution functions under the condition of a limited area of definition of a continuous random variable. All distribution functions used in the work are divided into three categories depending on the form in which entropy and its elasticity are presented. The first category includes distribution functions for which entropy and its elasticity can be determined analytically, namely: Simpson distribution, Right-angled and negatively skew version distribution, Right-angled and positively skew version distribution, Sine Wave Distribution, Ark – Sine Distribution Type I, Ark – Sine Distribution Type IІ, Ordinary Cosine Distribution, Raised Cosine Distribution, U-shaped parabolic distribution Type I, Semi-elliptical distribution, Ark – Sine Distribution Type II. Another category includes distribution functions for which entropy can be defined in the analytical group, its elasticity can be defined in the tabular part, namely: Truncated Normal Distribution, Kumaraswamy Distribution, Beta Distribution, Generalized Beta Distribution, Uniformly increasing distribution density, Ark-Sine Distribution Type III. The third category includes distribution functions for which entropy and its elasticity can be determined in tabular form. Basic information about the structure of the proposed calculator and examples of its application are provided. The method of determining the confidence interval of the point estimate of entropy is described. An example of using the calculator proposed in this message for planning an experiment related to entropy data analysis is given.