A Gompertz distribution for time scales

Authors

TOM CUCHTA
ROBERT JON NIICHEL
SABRINA STREIPERT

DOI

10.3906/mat-2003-101

Abstract

We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a $q$-geometric distribution of the second kind. Further, we find their $q$-binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.

Keywords

Time scales calculus, dynamic equations, difference equations, Gompertz, discrete q-distributions

First Page

185

Last Page

200

Recommended Citation

CUCHTA, TOM; NIICHEL, ROBERT JON; and STREIPERT, SABRINA (2021) "A Gompertz distribution for time scales," Turkish Journal of Mathematics: Vol. 45: No. 1, Article 12. https://doi.org/10.3906/mat-2003-101
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/12