Search results
Results From The WOW.Com Content Network
The Boltzmann distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibrium. It has a continuous analogue. Special cases include: The Gibbs distribution; The Maxwell–Boltzmann distribution; The Borel distribution
Any probability distribution can be decomposed as the mixture of a discrete, an absolutely continuous and a singular continuous distribution, [14] and thus any cumulative distribution function admits a decomposition as the convex sum of the three according cumulative distribution functions.
In probability theory and statistics, the probability distribution of a mixed random variable consists of both discrete and continuous components. A mixed random variable does not have a cumulative distribution function that is discrete or everywhere-continuous. An example of a mixed type random variable is the probability of wait time in a queue.
In general, distributions can be described as a discrete distribution (with a probability mass function), an absolutely continuous distribution (with a probability density), a singular distribution (with neither), or can be decomposed into a mixture of these. [1]
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
This distribution arises from the construction of a system of discrete distributions similar to that of the Pearson distributions for continuous distributions. [12] One can generate Student A(t | ν) samples by taking the ratio of variables from the normal distribution and the square-root of the χ² distribution.
The gamma distribution is a special case of the generalized gamma distribution, the generalized integer gamma distribution, and the generalized inverse Gaussian distribution. Among the discrete distributions, the negative binomial distribution is sometimes considered the discrete analog of the gamma distribution.
In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. [ 1 ]