On Mixed and Compound Mixed Poisson Distributions

Antzoulakos, Demetrios L.; Chadjiconstantinidis, Stathis

doi:10.1080/03461230110106525

Cited by 15 publications

(18 citation statements)

References 13 publications

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“…However, it could also be of interest to find more direct recursions for such functions. Such recursions were studied by Waldmann (1996) and more generally by Dhaene et al (1999), Chadjiconstantinidis (2003) and Antzoulakos and Chadjiconstantinidis (2004). For a review of such recursions see Sundt (2002) and the references therein.…”

Section: Remark 12 As Noted By Dementioning

confidence: 97%

Further improved recursions for a class of compound Poisson distributions

Chadjiconstantinidis¹,

Pitselis²

2009

Insurance: Mathematics and Economics

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Section: Remark 12 As Noted By Dementioning

confidence: 97%

Further improved recursions for a class of compound Poisson distributions

Chadjiconstantinidis¹,

Pitselis²

2009

Insurance: Mathematics and Economics

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“…Sundt (2002)). See also the recent papers Antzoulakos and Chadjiconstantinidis (2004) and Eisele (2006) for recursive evaluation of discrete random sums when M follows a mixed Poisson distribution or a phase-type distribution.…”

Section: Consider the Random Summentioning

confidence: 98%

Error bounds in approximations of random sums using gamma-type operators

Sangüesa

2008

Insurance: Mathematics and Economics

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“…For example, in Antzoulakos and Chadjiconstantinidis [1] , recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. In addition, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms.…”

Section: Introductionmentioning

confidence: 99%

On the distributions of two classes of multiple dependent aggregate claims

Wang

Yuen

Zhu

2008

Acta Math. Appl. Sin. Engl. Ser.

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In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24: 19-32(1994)] and Wang & Sobrero's [ASTIN Bulletin, 24: 161-166 (1994)] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution.Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29: 29-45 (1999)] and Ambagaspitiya [Insurance: Mathematics and Economics, 24: 301-308 (1999)]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution.

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On Mixed and Compound Mixed Poisson Distributions

Cited by 15 publications

References 13 publications

Further improved recursions for a class of compound Poisson distributions

Further improved recursions for a class of compound Poisson distributions

Error bounds in approximations of random sums using gamma-type operators

On the distributions of two classes of multiple dependent aggregate claims

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