Mills Ratio

Author

Eric W. Weisstein
December 16, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Statistics/MillsRatio.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MillsRatio.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Definition

((1-CDF[dist,x])/(PDF[dist,x]))

Examples

Normal Distribution

dist=NormalDistribution[μ,σ];

FullSimplify[((1-CDF[dist,x])/(PDF[dist,x]))]

FullSimplify[((1-CDF[dist,x])/(PDF[dist,x]))/.{μ->0,σ->1}]

ContinuedFractionK[k,z,{k,1,4}]//Factor

(1/(z+(2/(z+(3/(z+(4/z)))))))//Factor

(N[#1,100]&)[With[{n=1000,z=1/3+I/2},ContinuedFractionK[k,z,{k,1,n}]-((Sqrt[2/Pi]*(1/Erfc[z/Sqrt[2]]))/E^(z^2/2)-z)]]

ContinuedFractionK[k,z,{k,1,n}]