In the statistical literature, several discrete distributions have been developed so far for mod- eling non-negative integer-valued phenomena, yet there is still room for new counting models that adequately capture the diversity of real data sets. Here, we first discuss a count distri- bution derived as a discrete analogue of the continuous half-logistic distribution, which is obtained by preserving the expression of its survival function at each non-negative integer support point. The proposed discrete distribution has a mode at zero and allows for over- dispersion; these two features make it suitable for modeling purposes in many fields (e.g., insurance and ecology), when these conditions are satisfied by the data. In order to widen its spectrum of applications, a discrete analogue is also presented of the type I generalized half-logistic distribution (obtained by adding a shape parameter to the simple one-parameter half-logistic), which allows us to model count data whose mode is not necessarily zero. For these new count distributions, the main statistical properties are outlined, and parameter esti- mation along with related issues is discussed. Their feasibility is proved on two real data sets taken from the literature, which have already been fitted by other well-established count distributions. Finally, a possible application is illustrated in the insurance field, related to the exact/approximate determination of the distribution of the total claims amount through the well-known Panjer’s recursive formula, within the framework of collective risk models.

Discrete half-logistic distributions with applications in reliability and risk analysis / A. Barbiero, A. Hitaj. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (2024), pp. 1-31. [Epub ahead of print] [10.1007/s10479-023-05807-3]

### Discrete half-logistic distributions with applications in reliability and risk analysis

#### Abstract

In the statistical literature, several discrete distributions have been developed so far for mod- eling non-negative integer-valued phenomena, yet there is still room for new counting models that adequately capture the diversity of real data sets. Here, we first discuss a count distri- bution derived as a discrete analogue of the continuous half-logistic distribution, which is obtained by preserving the expression of its survival function at each non-negative integer support point. The proposed discrete distribution has a mode at zero and allows for over- dispersion; these two features make it suitable for modeling purposes in many fields (e.g., insurance and ecology), when these conditions are satisfied by the data. In order to widen its spectrum of applications, a discrete analogue is also presented of the type I generalized half-logistic distribution (obtained by adding a shape parameter to the simple one-parameter half-logistic), which allows us to model count data whose mode is not necessarily zero. For these new count distributions, the main statistical properties are outlined, and parameter esti- mation along with related issues is discussed. Their feasibility is proved on two real data sets taken from the literature, which have already been fitted by other well-established count distributions. Finally, a possible application is illustrated in the insurance field, related to the exact/approximate determination of the distribution of the total claims amount through the well-known Panjer’s recursive formula, within the framework of collective risk models.
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Count distribution; Discretization; Panjer’s formula; Survival function
Settore SECS-S/01 - Statistica
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
2024
19-gen-2024
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/1024770`