Rademacher distribution

Rademacher

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

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

<math> f(k) = \left\{\begin{matrix} 1/2 & \mbox {if }k=-1, \\

1/2 & \mbox {if }k=+1, \\ 0 & \mbox {otherwise.}\end{matrix}\right.</math>

The Rademacher distribution has been used in bootstrapping.

Related distributions

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

it:Variabile casuale di Rademacher