dgampois: Gamma-Poisson probability density

In rmcelreath/rethinking: Statistical Rethinking book package

Gamma-Poisson probability density

Description

Functions for computing density and producing random samples from a gamma-Poisson (negative-binomial) probability distribution.

Usage

dgampois( x , mu , scale , log=FALSE )
rgampois( n , mu , scale )

Arguments

x	Integer values to compute probabilies of
mu	Mean of gamma distribution
scale	Scale parameter of gamma distribution
log	If TRUE, returns log-probability instead of probability
n	Number of random observations to sample

Details

These functions provide density and random number calculations for gamma-Poisson observations. These functions use dnbinom and rnbinom internally, but convert the parameters from the mu and scale form. The size parameter of the negative-binomial is defined by mu/scale, and the prob parameter of the negative-binomial is the same as 1/(1+scale).

Author(s)

Richard McElreath

Examples

## Not run: 
data(Hurricanes)

# map model fit
# note exp(log_scale) to constrain scale to positive reals
m <- map(
    alist(
        deaths ~ dgampois( mu , exp(log_scale) ),
        log(mu) <- a + b*femininity,
        a ~ dnorm(0,100),
        b ~ dnorm(0,1),
        log_scale ~ dnorm(1,10)
    ),
    data=Hurricanes )

# map2stan model fit
# constraint on scale is passed via contraints list
m.stan <- map2stan(
    alist(
        deaths ~ dgampois( mu , scale ),
        log(mu) <- a + b*femininity,
        a ~ dnorm(0,100),
        b ~ dnorm(0,1),
        scale ~ dcauchy(0,2)
    ),
    data=Hurricanes,
    constraints=list(scale="lower=0"),
    start=list(scale=2) )

## End(Not run)

rmcelreath/rethinking documentation built on Sept. 18, 2023, 2:01 p.m.