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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

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

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

$$f(k) = \frac{1}{2} \left( \delta \left( k - 1 \right) + \delta \left( k + 1 \right) \right)$$

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.

Mathematics Encyclopedia