Generating Statistical Distributions using Fractional Differential Equations
Keywords:
Conformable fractional derivative, fractional derivative, fractional differential equation, fractional probability distribution, probability distribution, UD derivative.Abstract
In a recent paper of Dixit and Ujlayan (UD), a new fractional derivative is introduced as a convex combination of the function and its first derivative; that is Dα f(x) = (1 − α)f(x) + αf′(x).
In this article, a new technique of generating fractional continuous probability distributions by solving UD fractional differential equations that associated to well-known continous probability distributions is presented. In particular, the UD fractional probability distributions for the Exponential, Pareto, Lomax, and Levy distributions are generated. Finally, a real data application is considered for investigating the usefulness of the new fractional distributions. The results reveal that the proposed new fractional distribution performs better than the baseline distribution.
Key words and phrases. Conformable fractional derivative, fractional derivative, fractional differential equation, fractional probability distribution, probability distribution, UD derivative.
2010 Mathematics Subject Classification. 26A33; 60E05