Poisson Distributed Data

When to use poisson distributions

used to model count data

argument of poisson distribution

the mean, which is always equal to the variance

algebraic formula for poisson distributed data with covariate variables

Y_i = pois(exp(mx_i + c))

algebraic formula for poisson distributed data with factor variables

Y_i = pois(exp(ɑ_j + β_k + c))

what does this graph represent

poisson distributed data

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over-dispersed data

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zero-inflated data

residual deviance

chi-squared distributed with the residual degrees of freedom

solution to overdispersed data

negative binomial distribution

when overdispersion has occured

if the ratio of residual deviance to residual degrees of freedom is much more than 1