scholarly journals The Conditional Poisson Process and the Erlang and Negative Binomial Distributions

2017 ◽  
Vol 07 (01) ◽  
pp. 16-22
Author(s):  
Anurag Agarwal ◽  
Peter Bajorski ◽  
David L. Farnsworth ◽  
James E. Marengo ◽  
Wei Qian
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Binomial Distributions ◽  
Conditional Poisson

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 Fractional negative binomial and Pólya processes

2018 ◽  
Vol 38 (1) ◽  
pp. 77-101
Author(s):  
Palaniappan Vellai Samy ◽  
Aditya Maheshwari
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Random Variable ◽  
Infinitely Divisible ◽  
One Dimensional ◽  
Fractional Poisson Process ◽  
Negative Binomial Process ◽  
The One ◽  
Definition Of ◽  
Binomial Process

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

scholarly journals Poisson superposition processes

2015 ◽  
Vol 52 (04) ◽  
pp. 1013-1027
Author(s):  
Harry Crane ◽  
Peter Mccullagh
Keyword(s):  
Power Series ◽  
Poisson Process ◽  
Explicit Expression ◽  
Negative Binomial ◽  
Poisson Processes ◽  
Domain Restriction ◽  
Point Configuration ◽  
Point Configurations ◽  
Algebraic Properties ◽  
Formal Power

Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -valued sequences. From properties of Poisson processes as well as some algebraic properties of formal power series, we obtain an explicit expression for the Janossy measure of Poisson superposition processes, and we study their law under domain restriction. Examples of well-known Poisson superposition processes include compound Poisson, negative binomial, and permanental (boson) processes.

scholarly journals Counting processes with Bernštein intertimes and random jumps

2015 ◽  
Vol 52 (04) ◽  
pp. 1028-1044 ◽  
Author(s):  
Enzo Orsingher ◽  
Bruno Toaldo
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Negative Binomial ◽  
Counting Processes ◽  
Lévy Measure ◽  
Fractional Poisson Process ◽  
Independent Increments ◽  
Random Jumps ◽  
The Times ◽  
Passage Times

In this paper we consider point processes Nf (t), t > 0, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernštein functions f with Lévy measure v. We obtain the general expression of the probability generating functions Gf of Nf , the equations governing the state probabilities pk f of Nf , and their corresponding explicit forms. We also give the distribution of the first-passage times Tk f of Nf , and the related governing equation. We study in detail the cases of the fractional Poisson process, the relativistic Poisson process, and the gamma-Poisson process whose state probabilities have the form of a negative binomial. The distribution of the times of jumps with height lj () under the condition N(t) = k for all these special processes is investigated in detail.

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