scholarly journals On the Compound Generalized Poisson Distributions

1994 ◽  
Vol 24 (2) ◽  
pp. 255-263 ◽  
Author(s):  
R.S. Ambagaspitiya ◽  
N. Balakrishnan
Keyword(s):  
Integral Equation ◽  
Asymptotic Formula ◽  
Generating Functions ◽  
Recursive Formula ◽  
Basic Principles ◽  
Absolutely Continuous ◽  
Generalized Poisson Distribution ◽  
Generalized Poisson ◽  
Recursive Scheme ◽  
Arithmetic Distribution

AbstractGoovaerts and Kaas (1991) present a recursive scheme, involving Panjer's recursion, to compute the compound generalized Poisson distribution (CGPD). In the present paper, we study the CGPD in detail. First, we express the generating functions in terms of Lambert's W function. An integral equation is derived for the pdf of CGPD, when the claim severities are absolutely continuous, from the basic principles. Also we derive the asymptotic formula for CGPD when the distribution of claim severity satisfies certain conditions. Then we present a recursive formula somewhat different and easier to implement than the recursive scheme of Goovaerts and Kaas (1991), when the distribution of claim severity follows an arithmetic distribution, which can be used to evaluate the CGPD. We illustrate the usage of this formula with a numerical example.

scholarly journals Evaluating Compound Generalized Poisson Distributions Recursively

1991 ◽  
Vol 21 (2) ◽  
pp. 193-198 ◽  
Author(s):  
M. J. Goovaerts ◽  
R. Kaas
Keyword(s):  
Poisson Distribution ◽  
Generalized Poisson Distribution ◽  
Basic Properties ◽  
Generalized Poisson ◽  
Recursive Scheme ◽  
Poisson Distributions ◽  
Counting Distribution

AbstractIn this paper we give a recursive scheme, involving Panjer's recursion, to compute the distribution of a compound sum of integer claims, when the number of summands follows a Generalized Poisson distribution. Also, an elegant derivation is given for some basic properties of this counting distribution.

Bivariate generalized Poisson distribution with some applications

Metrika ◽  
1995 ◽  
Vol 42 (1) ◽  
pp. 127-138 ◽  
Author(s):  
Felix Famoye ◽  
P. C. Consul
Keyword(s):  
Poisson Distribution ◽  
Generalized Poisson Distribution ◽  
Generalized Poisson

scholarly journals Central values of additive twists of cuspidal L-functions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Asbjørn Christian Nordentoft
Keyword(s):  
Asymptotic Formula ◽  
Cusp Form ◽  
Dirichlet Character ◽  
Cusp Forms ◽  
Modular Symbols ◽  
Central Values ◽  
Arithmetic Distribution ◽  
Holomorphic Cusp Forms ◽  
Normally Distributed

Abstract Additive twists are important invariants associated to holomorphic cusp forms; they encode the Eichler–Shimura isomorphism and contain information about automorphic L-functions. In this paper we prove that central values of additive twists of the L-function associated to a holomorphic cusp form f of even weight k are asymptotically normally distributed. This generalizes (to k ≥ 4 {k\geq 4} ) a recent breakthrough of Petridis and Risager concerning the arithmetic distribution of modular symbols. Furthermore, we give as an application an asymptotic formula for the averages of certain “wide” families of automorphic L-functions consisting of central values of the form L ⁢ ( f ⊗ χ , 1 / 2 ) {L(f\otimes\chi,1/2)} with χ a Dirichlet character.

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