A Discrete Analogue of the Half-Logistic Distribution

Abstract

In lifetime modeling, the observed measurements are usually discrete in nature, because the values are measured to only a finite number of decimal places and cannot really constitute all points in a continuum. For example, the survival time of a cancer patient can be measured as the number of months he/she survives. Then, even if the lifetime (of a patient, a device, etc.) is intrinsically continuous, it is reasonable to consider its observations as coming from a discretized distribution generated from an underlying continuous model. In this work, a discrete random distribution, supported on the non-negative integers, is obtained from the continuous half-logistic distribution by using a well-established discretization technique, which preserves the functional form of the survival function. Its main statistical properties are explored, with a special focus on the shape of the probability mass function and the determination of the first two moments; we discuss and compare, both theoretically and empirically, two different methods for estimating its unique parameter. This discrete random distribution can be used for modeling data exhibiting excess of zeros and over-dispersion, which are features often met in the insurance and ecology fields: an example of application is illustrated. An extension of this discrete distribution is finally suggested, by considering the generalized half-logistic distribution, which introduces a second shape parameter allowing for greater flexibility.