The power binomial distribution: a flexible (two-parameter) finite probability distribution

2002 ◽  
Vol 18 (3) ◽  
pp. 219-224
Author(s):  
N. I. Fisher
Keyword(s):  
Probability Distribution ◽  
Binomial Distribution ◽  
Two Parameter

A Simple Modification of the Binomial Distribution

1960 ◽  
Vol 15 (06) ◽  
pp. 436-444
Author(s):  
S. W. Dharmadhikari
Keyword(s):  
Probability Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Simple Modification ◽  
Type Iii

Given any probability distribution, new distributions can be derived from it by assuming its parameters to follow some specific probability distributions. A simple example of this process is provided by the Poisson distributionP(r∣λ) =e-λλr/r! (r= o, 1, 2, …).If the parameterλis assumed to follow the Pearson's Type III lawthen the probability ofrsuccesses is obtained as

Asymptotics of the Hurwitz Binomial Distribution Related to Mixed Poisson Galton–Watson Trees

2001 ◽  
Vol 10 (3) ◽  
pp. 203-211 ◽  
Author(s):  
JÜRGEN BENNIES ◽  
JIM PITMAN
Keyword(s):  
Probability Distribution ◽  
Asymptotic Behaviour ◽  
Binomial Distribution ◽  
Random Tree ◽  
Binomial Theorem ◽  
Offspring Distribution

Hurwitz's extension of Abel's binomial theorem defines a probability distribution on the set of integers from 0 to n. This is the distribution of the number of non-root vertices of a fringe subtree of a suitably defined random tree with n + 2 vertices. The asymptotic behaviour of this distribution is described in a limiting regime in which the fringe subtree converges in distribution to a Galton–Watson tree with a mixed Poisson offspring distribution.

scholarly journals Theorizing Probability Distribution in Applied Statistics

2020 ◽  
Vol 1 (1) ◽  
pp. 79-95
Author(s):  
Indra Malakar
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Identical Condition ◽  
Random Variable ◽  
Fixed Number ◽  
Theoretical Knowledge ◽  
Applied Statistics ◽  
Discrete Random Variable

This paper investigates into theoretical knowledge on probability distribution and the application of binomial, poisson and normal distribution. Binomial distribution is widely used discrete random variable when the trails are repeated under identical condition for fixed number of times and when there are only two possible outcomes whereas poisson distribution is for discrete random variable for which the probability of occurrence of an event is small and the total number of possible cases is very large and normal distribution is limiting form of binomial distribution and used when the number of cases is infinitely large and probabilities of success and failure is almost equal.

scholarly journals A mechanistic model for the negative binomial distribution of single-cell mRNA counts

2019 ◽  
Author(s):  
Lisa Amrhein ◽  
Kumar Harsha ◽  
Christiane Fuchs
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Single Cell ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mechanistic Model ◽  
Steady State Probability ◽  
Degradation Models

SummarySeveral tools analyze the outcome of single-cell RNA-seq experiments, and they often assume a probability distribution for the observed sequencing counts. It is an open question of which is the most appropriate discrete distribution, not only in terms of model estimation, but also regarding interpretability, complexity and biological plausibility of inherent assumptions. To address the question of interpretability, we investigate mechanistic transcription and degradation models underlying commonly used discrete probability distributions. Known bottom-up approaches infer steady-state probability distributions such as Poisson or Poisson-beta distributions from different underlying transcription-degradation models. By turning this procedure upside down, we show how to infer a corresponding biological model from a given probability distribution, here the negative binomial distribution. Realistic mechanistic models underlying this distributional assumption are unknown so far. Our results indicate that the negative binomial distribution arises as steady-state distribution from a mechanistic model that produces mRNA molecules in bursts. We empirically show that it provides a convenient trade-off between computational complexity and biological simplicity.Graphical Abstract

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.

Probability and distributions

2020 ◽  
pp. 243-280
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Medical Statistics

Probability and probability distributions play a central part in medical statistics. This chapter defines what is meant by probability and describes the rules by which probabilities are combined. It then describes how the use of probability leads to the concept of a probability distribution and shows how these distributions are used in medical statistics. Examples are given of the use of key distributions: the Normal distribution, the binomial distribution, and the Poisson distribution.

Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

1973 ◽  
Vol 10 (04) ◽  
pp. 875-880 ◽  
Author(s):  
S. R. Paranjape ◽  
C. Park
Keyword(s):  
Lower Bound ◽  
Probability Distribution ◽  
Wiener Process ◽  
Two Parameter

Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.

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