Rademacher distribution

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Rademacher
Probability mass function
Cumulative distribution function
Parameters
Support	$k=\{-1,1\}\,$
Probability mass function (pmf)	$\begin{matrix} 1/2 & \mbox{for }k=-1 \\1/2 & \mbox{for }k=1 \end{matrix}$
Cumulative distribution function (cdf)	$\begin{matrix} 0 & \mbox{for }k<-1 \\1/2 & \mbox{for }-1<k<1\\1 & \mbox{for }k>1 \end{matrix}$
Mean	$0\,$
Median	$0\,$
Mode	N/A
Variance	$1\,$
Skewness	$0\,$
Excess kurtosis	$-2\,$
Entropy	$\ln(2)\,$
Moment-generating function (mgf)	$\cosh(t)\,$
Characteristic function	$\cos(t)\,$

In probability theory and statistics, the Rademacher distribution, named after Hans Rademacher is a discrete probability distribution which has a 50% chance for either 1 or -1. The probability mass function of this distribution is

$f(k) = \left\{\begin{matrix} 1/2 & \mbox {if }k=-1, \\ 1/2 & \mbox {if }k=+1, \\ 0 & \mbox {otherwise.}\end{matrix}\right.$

The Rademacher distribution has been used in bootstrapping.

[edit] Related distributions

Bernoulli distribution: If X has a Rademacher distribution then $\frac{X+1}{2}$ has a Bernoulli(1/2) distribution.

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Category: Discrete distributions

Rademacher distribution

From Wikipedia, the free encyclopedia

[edit] Related distributions

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