Recursions for compound phase distributions

Eisele, Karl-Theodor

doi:10.1016/j.insmatheco.2005.08.002

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Introduction2

Consider the Random Sum1

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2008

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Cited by 25 publications

(23 citation statements)

References 8 publications

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“…

We show how to generalize the result given in [Eisele, K.-Th., 2006. Recursions for compound phase distributions.

…”

mentioning

confidence: 52%

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Recursions for multivariate compound phase variables

Eisele¹

2008

Insurance: Mathematics and Economics

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“…

We show how to generalize the result given in [Eisele, K.-Th., 2006. Recursions for compound phase distributions.

…”

mentioning

confidence: 52%

“…We used this fact in Eisele (2006) to show a recursion principle of Panjer's type for univariate compound phase variables. In a different context, Hipp showed in Hipp (2006) that Panjer's recursion is reduced to one of a local depth if the severity distributions are of phase type.…”

Section: Introductionmentioning

confidence: 99%

Recursions for multivariate compound phase variables

Eisele¹

2008

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: 99%

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

Sangüesa

2008

Insurance: Mathematics and Economics

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“…Detailed discussions of continuous phase-type distributions can be found in [21] and [13]. Brief overviews of either discrete or continuous phase-type distributions and their properties can be found in [5,6,8,10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Inventory System with Postponed Demands and Infinite Pool in Discrete-Time Setup

Radhamani¹,

Devi²

2014

J. Oper. Res. Soc. China

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In this article, we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process. The inventory is replenished according to an ðs; SÞ policy, and the lead time is assumed to follow a discrete phase-type distribution. The demands that occur during stock-out periods either enter a pool which has an infinite capacity or leave the system with a predefined probability. The demands in the pool are selected one by one, if the on-hand inventory level is above s þ 1; and the interval time between any two successive selections is assumed to have a discrete phase-type distribution. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady-state case. We derive the system performance measures under steady state and using these measures, the total expected cost rate of the system is calculated. The impacts of arrival rate on the performance measures are graphically illustrated. Finally, we study the impact of cost on the optimal values of the total expected cost rate, inventory level and the reorder point.

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Recursions for compound phase distributions

Cited by 25 publications

References 8 publications

Recursions for multivariate compound phase variables

Recursions for multivariate compound phase variables

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

A Stochastic Inventory System with Postponed Demands and Infinite Pool in Discrete-Time Setup

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