A new discrete distrlbution, with applications to survival, dispersal and dispersion

Abstract

We describe a new discrete probability distribution with several useful properties for the analysis and modelling of survival processes and dispersion. First, the model can be used to describe survival processes with monotonically decreasing, constant, or increasing hazard functions, simply by tuning one parameter. Also, the model can describe counts that are overdispersed (contagious) or underdispersed, since the variance can exceed, equal, or be less than the mean. All of these properties are demonstrated both theoretically and with ecological examples, using ad-hoc parameter estimation techniques. Finally, the equations are tractable compared with, say, the negative binomial, and easily incorporated into larger models.

Keywords:

• discrete distributions
• survivorship
• dispersal
• dispersion
• hazard rate
• negative binomial distribution
• geometric distribution
• log series distribution
• discrete Pareto distribution
• discrete zeta distribution
• polylogarithm
• Lerch's function