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In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. [1] Poisson regression assumes the response variable Y has a Poisson distribution , and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters .
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In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
Hilbe [3] notes that "Poisson regression is traditionally conceived of as the basic count model upon which a variety of other count models are based." In a Poisson model, "… the random variable y {\displaystyle y} is the count response and parameter λ {\displaystyle \lambda } (lambda) is the mean.
In statistics, a fixed-effect Poisson model is a Poisson regression model used for static panel data when the outcome variable is count data. Hausman, Hall, and ...
HCMUSSH was formerly known as the College of Letters, University of Saigon (Vietnamese: Trường Đại học Văn khoa, Viện Đại học Sài Gòn). It is now the biggest research and training center in the field of social sciences and humanities in Southern Vietnam. In October 2021, HCMUSSH officially claimed their autonomy in the ...
The generalized functional linear model (GFLM) is an extension of the generalized linear model (GLM) that allows one to regress univariate responses of various types (continuous or discrete) on functional predictors, which are mostly random trajectories generated by a square-integrable stochastic processes.
There is no simple formula for the entropy of a Poisson binomial distribution, but the entropy is bounded above by the entropy of a binomial distribution with the same number parameter and the same mean. Therefore, the entropy is also bounded above by the entropy of a Poisson distribution with the same mean. [7]