Parameters Probability mass function Cumulative distribution function $k=\{-1,1\}\,$ $ \begin{matrix} 1/2 & \mbox{for }k=-1 \\1/2 & \mbox{for }k=1 \end{matrix}$  $ \begin{matrix} 0 & \mbox{for }k<-1 \\1/2 & \mbox{for }-11 \end{matrix}$  $0\,$ $0\,$ N/A $1\,$ $0\,$ $-2\,$ $\ln(2)\,$ $\cosh(t)\,$ $\cos(t)\,$

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.

Related distributions

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