On Markov-Pólya Distribution and the Katz Family of Distributions

Gathy, Maude; Lefèvre, Claude

doi:10.1080/03610920903427784

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A Claim Occurence Model1

Introduction1

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2010

2023

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Cited by 2 publications

(2 citation statements)

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“…Recently, Gathy and Lefèvre (2009) pointed out how to derive the classical Panjer recursion as a limit in an individual claim occurrence model with (anti-)imitation. In short, consider an individual who is subjected to a given number m of exposures to a certain risk, each exposure yielding either one claim or no claim.…”

Section: A Claim Occurence Modelmentioning

confidence: 99%

On the Lagrangian Katz family of distributions as a claim frequency model

Gathy

Lefèvre

2010

Insurance: Mathematics and Economics

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Section: A Claim Occurence Modelmentioning

confidence: 99%

On the Lagrangian Katz family of distributions as a claim frequency model

Gathy

Lefèvre

2010

Insurance: Mathematics and Economics

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“…The author in [18] showed that the LKD was a subclass of the generalized Polya-Eggenberger family of distributions. The authors in [19] obtained the LKD as a limiting distribution of the Markov-Polya distribution. The authors in [20] discussed the application of the LKD to time series data.…”

Section: Introductionmentioning

confidence: 99%

A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences

et al. 2023

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In this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the closed form expression of all its statistical characteristics, the LZTKD is proven to provide an adequate model for both underdispersed and overdispersed zero-truncated count datasets. Specifically, we show that the associated hazard rate function has increasing, decreasing, bathtub, or upside-down bathtub shapes. Moreover, we demonstrate that the LZTKD belongs to the Lagrangian distribution of the first kind. Then, applications of the LZTKD in statistical scenarios are explored. The unknown parameters are estimated using the well-reputed method of the maximum likelihood. In addition, the generalized likelihood ratio test procedure is applied to test the significance of the additional parameter. In order to evaluate the performance of the maximum likelihood estimates, simulation studies are also conducted. The use of real-life datasets further highlights the relevance and applicability of the proposed model.

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On Markov-Pólya Distribution and the Katz Family of Distributions

Cited by 2 publications

References 10 publications

On the Lagrangian Katz family of distributions as a claim frequency model

On the Lagrangian Katz family of distributions as a claim frequency model

A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences

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