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Standard Normal Distribution

Russ Lenth - email

summary

pdf, cdf, and quantile of the N(0,1) distribution

instructions

This adds basic functionality for the normal
distribution.

The pdf at z is the function
phi(z) = exp(-.5 z^2) / sqrt(2pi).

The cdf is the function
Phi(z) = integral phi(t)dt from t = -infinity to t = z.

The quantile is the solution z to the equation Phi(z) = p where p is the
value supplied.

The algorithm for the cdf is (26.2.16) in Abramowitz and Stegun,
which is accurate to +/- 1e-5.
(It'd be easy but bulkier to use (26.2.17), accurate to +/ -1e-8).
The quantile is obtained using the Tukey's lambda approximation
z = 4.92{p^.14 - (1-p)^.14} as a starter, and doing one Newton step.

code

RPN.1
[d]g1*Hne#'.39894228'*;
[p]g10<(nCpn1+:g1#'.33267'*1+tg1g1#'.9372980'*#'.1201676'-*#'.4361836'+*r2Cd*n1+);

[q]g1g1#'.14'Pr2n1+#'.14'P-#'4.92'*r2g2Cp-g2Cd/+;
"Normal dist"
"_p(x): pdf"Cd;
"_P(x): cdf"Cp;
"_Q(x): quantile"Cq;

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August 03, 2001
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