5 papers
The Zeta Tail Distribution: A Novel Event-Count Model
Michael R. Powers
We introduce the Zeta Tail probability distribution as a new model for random damage-event counts in risk analysis. Although a natural analogue of the Geometric$\le…
Conjunctions of Three "Euler Constants" in Poisson-Related Expressions
Michael R. Powers
Three mathematical constants bear the name of the venerable Leonhard Euler: Euler's number, ; the Euler-Mascheroni constant, ; and the Euler-Gom…
A Sequence of Nested Exponential Random Variables with Connections to Two Constants of Euler
Michael R. Powers
We investigate a recursively generated sequence of random variables that begins with an Exponential random variable with parameter (i.e., inverse-mean) 1, and continues with additi…
Heavy-Tailed Loss Frequencies from Mixtures of Negative Binomial and Poisson Counts
Jiansheng Dai, Ziheng Huang, Michael R. Powers +1
Heavy-tailed random variables have been used in insurance research to model both loss frequencies and loss severities, with substantially more emphasis on the latter. In the presen…
Characterizing the Zeta Distribution via Continuous Mixtures
Jiansheng Dai, Ziheng Huang, Michael R. Powers +1
We offer two novel characterizations of the Zeta distribution: first, as tractable continuous mixtures of Negative Binomial distributions (with fixed shape parameter, r > 0), and s…