Logistic Distribution

Author

Eric W. Weisstein
June 23, 2006

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

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

©2006 Wolfram Research, Inc. except for portions noted otherwise

Usage

?LogisticDistribution

Plot

Show[GraphicsArray[Plot[#[LogisticDistribution[0,1],x],{x,-10,10},AxesLabel->TraditionalForm/@{x,#[x]},
PlotStyle->Red,Ticks->None,DisplayFunction->Identity,PlotRange->All]&/@{PDF,CDF}]]

Stats

Stats[LogisticDistribution[m,b],x]//StatsForm//TraditionalForm

Moments

Normalization

Integrate[PDF[LogisticDistribution[m,b],x],{x,-∞,∞},Assumptions->b>0]

Raw

v5.2

Integrate[PDF[LogisticDistribution[m,b],x](x^n),{x,-∞,∞},Assumptions->b>0&&n>0&&n∈Integers]

Table[Integrate[PDF[LogisticDistribution[m,b],x](x^n),{x,-∞,∞},Assumptions->b>0],{n,0,3}]

v6

Central

v5.2

Integrate[PDF[LogisticDistribution[m,b],x](((x-m))^n),{x,-∞,∞},Assumptions->b>0&&n>0&&n∈Integers]

v6

Integrate[PDF[LogisticDistribution[m,b],x](((x-m))^n),{x,-∞,∞},Assumptions->b>0&&n>0&&n∈Integers]