scholarly journals Classifying Documents with Poisson Mixtures

2014 ◽  
Vol 2 (4) ◽  
Author(s):  
Hiroshi Ogura ◽  
Hiromi Amano ◽  
Masato Kondo
Keyword(s):  
Poisson Mixtures

On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution

1977 ◽  
Vol 82 (2) ◽  
pp. 297-300 ◽  
Author(s):  
A. V. Godambe
Keyword(s):  
Gamma Distribution ◽  
Exponential Type ◽  
Similar Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Poisson Mixture ◽  
Mixing Distribution ◽  
Poisson Mixtures ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.

Poisson mixtures

1995 ◽  
Vol 1 (2) ◽  
pp. 163-190 ◽  
Author(s):  
Kenneth W. Church ◽  
William A. Gale
Keyword(s):  
Negative Binomial ◽  
Probability Distributions ◽  
Hidden Variables ◽  
Heterogeneous Structure ◽  
Text Compression ◽  
Inverse Document Frequency ◽  
Poisson Mixtures ◽  
Document Frequency ◽  
Wide Range ◽  
Better Than

AbstractShannon (1948) showed that a wide range of practical problems can be reduced to the problem of estimating probability distributions of words and ngrams in text. It has become standard practice in text compression, speech recognition, information retrieval and many other applications of Shannon's theory to introduce a “bag-of-words” assumption. But obviously, word rates vary from genre to genre, author to author, topic to topic, document to document, section to section, and paragraph to paragraph. The proposed Poisson mixture captures much of this heterogeneous structure by allowing the Poisson parameter θ to vary over documents subject to a density function φ. φ is intended to capture dependencies on hidden variables such genre, author, topic, etc. (The Negative Binomial is a well-known special case where φ is a Г distribution.) Poisson mixtures fit the data better than standard Poissons, producing more accurate estimates of the variance over documents (σ2), entropy (H), inverse document frequency (IDF), and adaptation (Pr(x ≥ 2/x ≥ 1)).

scholarly journals Experience rating with Poisson mixtures

2015 ◽  
Vol 9 (2) ◽  
pp. 304-321 ◽  
Author(s):  
Garfield O. Brown ◽  
Winston S. Buckley
Keyword(s):  
Life Insurance ◽  
Dirichlet Process ◽  
Posterior Probability ◽  
Mixture Distribution ◽  
Reversible Jump ◽  
Dirichlet Process Prior ◽  
Poisson Mixtures ◽  
Group Life ◽  
Insurance Portfolio ◽  
Poisson Mixture Model

AbstractWe propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

scholarly journals On runs, bivariate Poisson mixtures and distributions that arise in Bernoulli arrays

2014 ◽  
Vol 19 (0) ◽  
Author(s):  
Éric Marchand ◽  
Djilali Ait Aoudia ◽  
François Perron ◽  
Latifa Ben Hadj Slimene
Keyword(s):  
Poisson Mixtures

Poisson approximation of multivariate Poisson mixtures

2003 ◽  
Vol 40 (02) ◽  
pp. 376-390 ◽  
Author(s):  
Bero Roos
Keyword(s):  
Total Variation ◽  
Poisson Approximation ◽  
Upper Bounds ◽  
Risk Theory ◽  
Total Variation Distance ◽  
Poisson Mixtures ◽  
Poisson Distributions ◽  
Variation Distance

We show how good multivariate Poisson mixtures can be approximated by multivariate Poisson distributions and related finite signed measures. Upper bounds for the total variation distance with applications to risk theory and generalized negative multinomial distributions are given. Furthermore, it turns out that the ideas used in this paper also lead to improvements in the Poisson approximation of generalized multinomial distributions.

Analysis of Long-Tailed Count Data by Poisson Mixtures

2005 ◽  
Vol 34 (3) ◽  
pp. 557-573 ◽  
Author(s):  
Ramesh C. Gupta ◽  
S.H. Ong
Keyword(s):  
Count Data ◽  
Poisson Mixtures

scholarly journals Estimating the real-time case fatality rate of COVID-19 using Poisson mixtures model

2020 ◽  
Author(s):  
Paul H. Lee
Keyword(s):  
Real Time ◽  
Case Fatality Rate ◽  
Early Stage ◽  
Case Fatality ◽  
Hubei Province ◽  
Fatality Rate ◽  
The Real ◽  
Poisson Mixtures

ABSTRACTWe proposed using Poisson mixtures model that utilized data of deaths, recoveries, and total confirmed cases in each day since the outbreak. We demonstrated that our CFR estimates for Hubei Province and other parts of China were superior to the simple CFR estimators in the early stage of COVID-19 outbreak.

Sign in / Sign up

Export Citation Format

Share Document