scholarly journals A generalized negative binomial distribution based on an extended Poisson process

2010 ◽  
Vol 24 (1) ◽  
pp. 91-99 ◽  
Author(s):  
Luis Ernesto Bueno Salasar ◽  
José Galvão Leite ◽  
Francisco Louzada Neto
Keyword(s):  
Poisson Process ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

scholarly journals On hypergeometric generalized negative binomial distribution

2002 ◽  
Vol 29 (12) ◽  
pp. 727-736 ◽  
Author(s):  
M. E. Ghitany ◽  
S. A. Al-Awadhi ◽  
S. L. Kalla
Keyword(s):  
Recurrence Relation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution ◽  
The Right ◽  
Three Term Recurrence Relation

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.

scholarly journals On A Model for the Claim Number Process

1988 ◽  
Vol 18 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Matti Ruohonen
Keyword(s):  
Structure Function ◽  
Poisson Process ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Credibility Theory ◽  
Gamma Model ◽  
Function Fitting ◽  
Claim Number ◽  
Two Parameter

AbstractA model for the claim number process is considered. The claim number process is assumed to be a weighted Poisson process with a three-parameter gamma distribution as the structure function. Fitting of this model to several data encountered in the literature is considered, and the model is compared with the two-parameter gamma model giving the negative binomial distribution. Some credibility theory formulae are also presented.

A characterization of the gamma distribution by the negative binomial distribution

1980 ◽  
Vol 17 (04) ◽  
pp. 1138-1144 ◽  
Author(s):  
Jan Engel ◽  
Mynt Zijlstra
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Gamma Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
One To One

It is proved that for a Poisson process there exists a one-to-one relation between the distribution of the random variable N(Y) and the distribution of the non-negative random variable Y. This relation is used to characterize the gamma distribution by the negative binomial distribution. Furthermore it is applied to obtain some characterizations of the exponential distribution.

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