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October 17, 2025Open Access

A Characterization of the Logistic q-Distribution

Key Points

The logistic q-distribution demonstrates unique properties through its probability density function and cumulative distribution function.
Characterization involves deriving the mean and variance, along with the introduction of the q-Fourier transform.
A new q-differential equation in quantum calculus aids in fully understanding the logistic q-distribution's characteristics.
Connections to exponential q-distributions are defined, emphasizing the logistic q-distribution's place within the broader framework.

Abstract

The current research paper investigates the logistic q−distribution q−L(0, 1) from a pro- babilistic perspective. Its unique characteristics lie in its probability density function (pdf), cumulative distribution function (cdf), mean, and variance. We introduce the q−Fourier transform and a new q−differential equation within the framework of quantum calculus and provide its solution in order to facilitate the characterization of the logistic q−distribution. A characterization of the relationship between the logistic q−distribution and exponential q−distributions is determined via the cumulative distribution function (cdf).

A Characterization of the Logistic q-Distribution

Key Points

Abstract

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