[R] Derivative of the probit

[(Ted Harding)]

On 06-May-10 20:40:30, Andrew Redd wrote:
> Is there a function to compute the derivative of the probit (qnorm)
> function
> in R, or in any of the packages?
> 
> Thanks,
> -Andrew

I don't think so (though stand to be corrected). However, it would
be straightforward to write one.

For simplicity of notation:
  P(x) = pnorm(x)
  Q(p) = qnrom(p)
  D(x) = dnorm(x)
  "'" stands for derivative.

Then

  P'(x) = D(x)

  P(Q(p)) = p

Differentiate w.r.to p:

  P'(Q(p))*Q'(p) = 1

  Q'(p) = 1/P'(Q(p)) = 1/D(Q(p))

Hence:

  dqnorm <- function(p){ 1/dnorm(qnorm(p)) }

(I think that's right ... )

Ted.

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Date: 06-May-10                                       Time: 22:23:53
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