Interface of Special Functions and Statistics
Sudesh Pundir · IOSR Journal of Mathematics · 2025
In the last two to three decades, significant research has focused on special functions related to statistical distributions. This includes the Generalized Hurwitz-Lerch Zeta Beta type-2 distributions and Gamma distribution, generalized hypergeometric distributions, Parabolic cylinder distribution, generalized Hurwitz Zeta Beta prime distributions, Mathieu distribution, Plank distribution, Mittag-Leffler distribution, Hurwitz Lerch Zeta distribution. Furthermore, the special cases explored include the Zipf-Mandelbrot distribution, Lotka distribution, Good distribution, Logarithmic Series distribution, right truncated form of the HLZ distribution and Estoup distribution. The study explores the properties and statistical measures like moment generating function, distribution function, survivor function, Hazard rate function, mean residue life function, characteristic function, probability generating function, likelihood equations result in method of moments.