Three generalised negative Binomial Distributions

1975 ◽  
Vol 17 (5) ◽  
pp. 286-302 ◽  
Author(s):  
I. G. Plunkett ◽  
G. C. Jain
Keyword(s):  
Negative Binomial ◽  
Binomial Distributions

scholarly journals INFLUENCE OF STATISTICAL FLUCTUATIONS ON K/π RATIOS IN RELATIVISTIC HEAVY ION COLLISIONS

2001 ◽  
Vol 16 (07) ◽  
pp. 1227-1235 ◽  
Author(s):  
C. B. YANG ◽  
X. CAI
Keyword(s):  
Negative Binomial ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Relative Variance ◽  
Ion Collisions ◽  
Statistical Fluctuations ◽  
Binomial Distributions ◽  
The Mean ◽  
Multiplicity Distributions ◽  
Statistical Background

The influence of pure statistical fluctuations on K/π ratio is investigated in an event-by-event way. Poisson and the modified negative binomial distributions are used as the multiplicity distributions since they both have statistical background. It is shown that the distributions of the ratio in these cases are Gaussian, and the mean and relative variance are given analytically.

scholarly journals EXPANSION IN BELL POLYNOMIALS OF THE DISTRIBUTION OF THE TOTAL CLAIM AMOUNT WITH WEIBULL-DISTRIBUTED CLAIM SIZES

2008 ◽  
Vol 49 (4) ◽  
pp. 495-501
Author(s):  
RAMON LACAYO
Keyword(s):  
Random Number ◽  
Negative Binomial ◽  
Claim Amount ◽  
Bell Polynomials ◽  
Total Claim Amount ◽  
Binomial Distributions ◽  
Probabilistic Distribution ◽  
Satisfactory Model ◽  
Total Claim ◽  
Fixed Period

AbstractThe total claim amount for a fixed period of time is, by definition, a sum of a random number of claims of random size. In this paper we explore the probabilistic distribution of the total claim amount for claims that follow a Weibull distribution, which can serve as a satisfactory model for both small and large claims. As models for the number of claims we use the geometric, Poisson, logarithmic and negative binomial distributions. In all these cases, the densities of the total claim amount are obtained via Laplace transform of a density function, an expansion in Bell polynomials of a convolution and a subsequent Laplace inversion.

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