Rademacher distribution

Rademacher
Support k \in \{-1,1\}\,
PMF f(k) = \begin{cases} 1/2, & k = -1 \\ 1/2, & k = 1 \end{cases}
CDF F(k) = \begin{cases} 0, & k < -1 \\ 1/2, & -1 \leq k < 1 \\ 1, & k \geq 1 \end{cases}
Mean 0\,
Median 0\,
Mode N/A
Variance 1/4\,
Skewness 0\,
Ex. kurtosis -2\,
Entropy \ln(2)\,
MGF \cosh(t)\,
CF \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=%2B1, \\ 0 & \mbox {otherwise.}\end{matrix}\right.

it can be also written, in term of the Dirac delta function, as

f(k) = \frac{1}{2} \left( \delta \left( k - 1 \right) %2B \delta \left( k %2B 1 \right) \right)

The Rademacher distribution has been used in bootstrapping.

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