Abstract
In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.
Highlights
This paper deals with the asymptotic behavior of the Hausdorff distance between Heaviside function and some novel distribution functions
We study the asymptotic behavior of the Hausdorff distance between Heaviside function and the pliant probability distribution function
It can be seen that the proven bottom estimates for the value of Hausdorff distance d is reliable in approximation of shifted Heaviside function ht0 (t) and the Omega CDF function F (t; α, β, m)
Summary
This paper deals with the asymptotic behavior of the Hausdorff distance between Heaviside function and some novel distribution functions. His work and achievements are connected to the approximation of functions with respect to Hausdorff distance. One of the important properties is that the omega function ωm β (α, β, m ∈ R, β, m > 0) and the exponential function f (x) = eαx (α, β ∈ R, β > 0) may be derived from a common differential equation. Some probability distributions, which formulas include exponential terms, can be approximated using this function, for example, the well-known. We study the asymptotic behavior of the Hausdorff distance between Heaviside function and the pliant probability distribution function.
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