Rademacher distribution
Encyclopedia
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
it can be also written, in term of the Dirac delta function, as
The Rademacher distribution has been used in bootstrapping
.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the Rademacher distribution (named after Hans Rademacher
Hans Rademacher
Hans Adolph Rademacher was a German mathematician, known for work in mathematical analysis and number theory.-Biography:...
) is a discrete probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
which has a 50% chance for either 1 or -1. The probability mass function
Probability mass function
In probability theory and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value...
of this distribution is
it can be also written, in term of the Dirac delta function, as
The Rademacher distribution has been used in bootstrapping
Resampling (statistics)
In statistics, resampling is any of a variety of methods for doing one of the following:# Estimating the precision of sample statistics by using subsets of available data or drawing randomly with replacement from a set of data points # Exchanging labels on data points when performing significance...
.
Related distributions
- Bernoulli distribution: If X has a Rademacher distribution then
has a Bernoulli(1/2) distribution.