Deriving Probabilistic SVM Kernels from Exponential Family Approximations to Multivariate Distributions for Count Data

2019 ◽  
pp. 125-153
Author(s):  
Nuha Zamzami ◽  
Nizar Bouguila
Keyword(s):  
Count Data ◽  
Exponential Family ◽  
Multivariate Distributions

scholarly journals A discrete multivariate distribution resulting from the law of small numbers

2006 ◽  
Vol 43 (03) ◽  
pp. 852-866 ◽  
Author(s):  
Nobuaki Hoshino
Keyword(s):  
Count Data ◽  
Exponential Family ◽  
Divisible Distribution ◽  
Multivariate Distribution ◽  
Inverse Gaussian ◽  
Real Numbers ◽  
Infinitely Divisible ◽  
The Law ◽  
Positive Integers ◽  
New Distribution

In the present article we derive a new discrete multivariate distribution using a limiting argument that is essentially the same as the law of small numbers. The distribution derived belongs to an exponential family, and randomly partitions positive integers. The facts shown about the distribution are useful in many fields of application involved with count data. The derivation parallels that of the Ewens distribution from the gamma distribution, and the new distribution is produced from the inverse Gaussian distribution. The method employed is regarded as the discretization of an infinitely divisible distribution over nonnegative real numbers.

scholarly journals A review of multivariate distributions for count data derived from the Poisson distribution

2017 ◽  
Vol 9 (3) ◽  
pp. e1398 ◽  
Author(s):  
David I. Inouye ◽  
Eunho Yang ◽  
Genevera I. Allen ◽  
Pradeep Ravikumar
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Multivariate Distributions

scholarly journals A flexible multivariate model for high-dimensional correlated count data

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Alexander D. Knudson ◽  
Tomasz J. Kozubowski ◽  
Anna K. Panorska ◽  
A. Grant Schissler
Keyword(s):  
Stochastic Model ◽  
Rna Sequencing ◽  
Count Data ◽  
Negative Binomial ◽  
Copula Function ◽  
Multivariate Model ◽  
High Dimensional ◽  
Sequencing Data ◽  
Multivariate Distributions ◽  
Dimensional Simulation

AbstractWe propose a flexible multivariate stochastic model for over-dispersed count data. Our methodology is built upon mixed Poisson random vectors (Y1,…,Yd), where the {Yi} are conditionally independent Poisson random variables. The stochastic rates of the {Yi} are multivariate distributions with arbitrary non-negative margins linked by a copula function. We present basic properties of these mixed Poisson multivariate distributions and provide several examples. A particular case with geometric and negative binomial marginal distributions is studied in detail. We illustrate an application of our model by conducting a high-dimensional simulation motivated by RNA-sequencing data.

scholarly journals A Weighted Poisson Distribution for Underdispersed Count Data

2021 ◽  
Vol 10 (4) ◽  
pp. 157
Author(s):  
Chedly Gelin Louzayadio ◽  
Rodnellin Onesime Malouata ◽  
Michel Diafouka Koukouatikissa
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Exponential Family ◽  
Discrete Distribution ◽  
Random Variable ◽  
Poisson Random Variable ◽  
Weighted Version ◽  
Poisson Variable ◽  
Two Parameter ◽  
New Distribution

In this paper, we present a new weighted Poisson distribution for modeling underdispersed count data. Weighted Poisson distribution occurs naturally in contexts where the probability that a particular observation of Poisson variable enters the sample gets multiplied by some non-negative weight function. Suppose a realization y of Y a Poisson random variable enters the investigator’s record with probability proportional to w(y): Clearly, the recorded y is not an observation on Y, but on the random variable Yw, which is said to be the weighted version of Y. This distribution a two-parameter is from the exponential family, it includes and generalizes the Poisson distribution by weighting. It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000). We present some moment properties and we estimate its parameters. One classical example is considered to compare the fits of this new distribution with the extended Poisson distribution.

scholarly journals A discrete multivariate distribution resulting from the law of small numbers

2006 ◽  
Vol 43 (3) ◽  
pp. 852-866 ◽  
Author(s):  
Nobuaki Hoshino
Keyword(s):  
Count Data ◽  
Exponential Family ◽  
Divisible Distribution ◽  
Multivariate Distribution ◽  
Inverse Gaussian ◽  
Real Numbers ◽  
Infinitely Divisible ◽  
The Law ◽  
Positive Integers ◽  
New Distribution

In the present article we derive a new discrete multivariate distribution using a limiting argument that is essentially the same as the law of small numbers. The distribution derived belongs to an exponential family, and randomly partitions positive integers. The facts shown about the distribution are useful in many fields of application involved with count data. The derivation parallels that of the Ewens distribution from the gamma distribution, and the new distribution is produced from the inverse Gaussian distribution. The method employed is regarded as the discretization of an infinitely divisible distribution over nonnegative real numbers.

Regression Analysis of Count Data

1998 ◽  
Author(s):  
A. Colin Cameron ◽  
Pravin K. Trivedi
Keyword(s):  
Regression Analysis ◽  
Count Data

Analyzing discontinuities in longitudinal count data: A multilevel generalized linear mixed model.

2020 ◽  
Author(s):  
James L. Peugh ◽  
Sarah J. Beal ◽  
Meghan E. McGrady ◽  
Michael D. Toland ◽  
Constance Mara
Keyword(s):  
Count Data ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Model ◽  
Longitudinal Count Data
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