Rademacher distribution

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.

Related distributions

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

	Probability distributions []
	Univariate	Multivariate
Discrete:	Benford • Bernoulli • binomial • Boltzmann • categorical • compound Poisson • discrete phase-type • degenerate • Gauss-Kuzmin • geometric • hypergeometric • logarithmic • negative binomial • parabolic fractal • Poisson • Rademacher • Skellam • uniform • Yule-Simon • zeta • Zipf • Zipf-Mandelbrot	Ewens • multinomial • multivariate Polya
Continuous:	Beta • Beta prime • Cauchy • chi-square • Dirac delta function • Coxian • Erlang • exponential • exponential power • F • fading • Fermi-Dirac • Fisher's z • Fisher-Tippett • Gamma • generalized extreme value • generalized hyperbolic • generalized inverse Gaussian • Half-logistic • Hotelling's T-square • hyperbolic secant • hyper-exponential • hypoexponential • inverse chi-square (scaled inverse chi-square) • inverse Gaussian • inverse gamma (scaled inverse gamma) • Kumaraswamy • Landau • Laplace • Lévy • Lévy skew alpha-stable • logistic • log-normal • Maxwell-Boltzmann • Maxwell speed • Nakagami • normal (Gaussian) • normal-gamma • normal inverse Gaussian • Pareto • Pearson • phase-type • polar • raised cosine • Rayleigh • relativistic Breit-Wigner • Rice • shifted Gompertz • Student's t • triangular • truncated normal • type-1 Gumbel • type-2 Gumbel • uniform • Variance-Gamma • Voigt • von Mises • Weibull • Wigner semicircle • Wilks' lambda	Dirichlet • Generalized Dirichlet distribution . inverse-Wishart • Kent • matrix normal • multivariate normal • multivariate Student • von Mises-Fisher • Wigner quasi • Wishart
Miscellaneous:	bimodal • Cantor • conditional • equilibrium • exponential family • Infinite divisibility (probability) • location-scale family • marginal • maximum entropy • posterior • prior • quasi • sampling • singular

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Rademacher distribution

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