zeta: Function `log(2*P(x))' and its derivatives

Description

The function log(2 P(x)) and its derivatives up to order 4, if P(x) denotes the standard normal distribution function.

Usage

zeta(k, x)

Arguments

an integer scalar between 0 and 4.

a vector. Missing values (NAs) are allowed, but Infs are not.

Value

a vector; this is the k-th order derivative evaluated at x

Details

k denotes the order of the derivative. If k is 0, the function is evaluated, using pnorm(x) for x>-35, an asymptotic expansion otherwise. For k between 1 and 4, the derivative of that order is evaluated. If k>4, an error message is issued.

This function is used by sn.dev and msn.dev, among others.

Examples

Run this code

y <- zeta(2,seq(-20,20,by=0.5))

for(i in 0:4) 
      curve(zeta(i,x),-1, 4, col = i+1, add = i > 0)