Stable evaluation of difference between Poisson c.d.f.s

Evaluates the difference between two Poisson cumulative distribution functions avoiding cancellation error.

dppois(y0,y1,mu,log.p=TRUE)

Arguments

y0

vector of lower values at which to evaluate Poisson distribution function.

y1

vector of upper values at which to evaluate Poisson distribution function.

mu

vector giving Poisson means

log.p

set to FALSE to compute on probability scale.

Details

Equivalent to log(ppois(y1,mu)-ppois(y0,mu)), but stable when y0 and y1 are highly improbable and in the same tail of the distribution (avoids cancellation to log(0)).

Author

Simon N. Wood simon.wood@r-project.org

Examples

require(mgcv)
n <- 10
mu <- rep(2,n)
y0 <- c(0:5,10,23,0,2)
y1 <- c(1:6,11,1000,100,40)
dppois(y0,y1,mu)
#>  [1]  -1.3068528  -1.3068528  -1.7123179  -2.4054651  -3.3217558  -4.4203681
#>  [7] -11.8776889 -40.0661024  -0.1454135  -1.1291016
log(ppois(y1,mu)-ppois(y0,mu))
#>  [1]  -1.3068528  -1.3068528  -1.7123179  -2.4054651  -3.3217558  -4.4203681
#>  [7] -11.8776889        -Inf  -0.1454135  -1.1291016