Translated Logarithmic Lambert Function and its Applications to Three-Parameter Entropy

TL;DR

This paper introduces the translated logarithmic Lambert function, explores its mathematical properties, and applies it to derive the probability distribution of three-parameter entropy, expanding tools for entropy analysis.

Contribution

The paper defines the translated logarithmic Lambert function, analyzes its properties, and applies it to derive the distribution of three-parameter entropy, a novel approach in entropy research.

Findings

Derived the probability distribution of three-parameter entropy.

Analyzed the derivative, integral, and asymptotic behavior of the function.

Provided series expansion and real branches of the function.

Abstract

The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function. Moreover, the probability distribution of the three-parameter entropy is derived which is expressed in terms of the translated logarithmic Lambert function.