28.1.107 LogNormal

Function

y=y_0+\frac A{\sqrt{2\pi }wx}e^{\frac{-\left[ \ln \frac x{xc}\right] ^2}{2w^2}}

Brief Description

Probability density function of random variable whose logarithm is normally distributed.

Sample Curve

LogNormal.png

Parameters

Number: 4

Names: y0, xc, w, A

Meanings: y0 = offset, xc = center, w = log standard deviation, A = area

Lower Bounds: xc > 0, w > 0

Upper Bounds: none

Derived Parameters

Mean: mu = exp(ln(xc)+1/2*w^2)

Standard Deviation: sigma = exp(ln(xc)+1/2*w^2)*sqrt(exp(w^2)-1)

Script Access

nlf_lognormal(x,y0,xc,w,A)

Function File

FITFUNC\LOGNORM.FDF

Category

Statistics, PFW, Peak Functions, Origin Basic Functions