mgcv (version 1.9-1)

dpnorm: Stable evaluation of difference between normal c.d.f.s

Description

Evaluates the difference between two \(N(0,1)\) cumulative distribution functions avoiding cancellation error.

Usage

dpnorm(x0,x1)

Arguments

x0

vector of lower values at which to evaluate standard normal distribution function.

x1

vector of upper values at which to evaluate standard normal distribution function.

Author

Simon N. Wood

Details

Equivalent to pnorm(x1)-pnorm(x0), but stable when x0 and x1 values are very close, or in the upper tail of the standard normal.

Examples

require(mgcv)
x <- seq(-10,10,length=10000)
eps <- 1e-10
y0 <- pnorm(x+eps)-pnorm(x) ## cancellation prone
y1 <- dpnorm(x,x+eps)       ## stable
## illustrate stable computation in black, and
## cancellation prone in red...
par(mfrow=c(1,2),mar=c(4,4,1,1))
plot(log(y1),log(y0),type="l")
lines(log(y1[x>0]),log(y0[x>0]),col=2)
plot(x,log(y1),type="l")
lines(x,log(y0),col=2)