A compound of the generalized negative binomial distribution with the generalized beta distribution

2004 ◽  
Vol 2 (4) ◽  
pp. 527-537
Author(s):  
Tadeusz Gerstenkorn
Keyword(s):  
Beta Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution ◽  
Generalized Beta 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 Generalized distributions of orderkassociated with success runs in Bernoulli trials

2003 ◽  
Vol 2003 (13) ◽  
pp. 801-815
Author(s):  
Gregory A. Tripsiannis ◽  
Afroditi A. Papathanasiou ◽  
Andreas N. Philippou
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Bernoulli Trials ◽  
Generalized Distributions ◽  
Polya Distribution ◽  
Generalized Negative Binomial Distribution ◽  
Order And Type ◽  
Special Case ◽  
New Distribution

In a sequence of independent Bernoulli trials, by counting multidimensional lattice paths in order to compute the probability of a first-passage event, we derive and study a generalized negative binomial distribution of orderk, typeI, which extends to distributions of orderk, the generalized negative binomial distribution of Jain and Consul (1971), and includes as a special case the negative binomial distribution of orderk, typeI, of Philippou et al. (1983). This new distribution gives rise in the limit to generalized logarithmic and Borel-Tanner distributions and, by compounding, to the generalized Pólya distribution of the same order and type. Limiting cases are considered and an application to observed data is presented.

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