 Probability Distributions - Maple Programming Help

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Probability Distributions

 This help page describes the probability distributions provided in the Statistics package, how to construct random variables using these distributions and the functions that are typically used in conjunction with these distributions.

Constructors

 • The constructors are used to create objects that wrap distributions.  However, most functions generally allow access to the distributions directly through their inert form.

 create a non-integer discrete distribution create new distribution create new random variable

Discrete Distributions

 • Discrete distributions have nonzero probability only at discrete points.  Discrete distributions are defined by their probability function rather than by their probability density function in order to avoid singularities.

 Bernoulli distribution binomial distribution discrete uniform distribution empirical distribution geometric distribution hypergeometric distribution negative binomial (Pascal) distribution Poisson distribution probability table

Continuous Distributions

 • Continuous distributions are defined along the real line by their probability density function.

 beta distribution Cauchy distribution chi-square distribution Erlang distribution error (exponential power) distribution exponential distribution Fisher f-distribution gamma distribution Gumbel distribution inverse Gaussian (Wald) distribution Laplace distribution logistic distribution log normal distribution Maxwell distribution Moyal distribution noncentral beta distribution noncentral chi-square distribution noncentral f-distribution noncentral t-distribution normal (Gaussian) distribution Pareto distribution power distribution Rayleigh distribution Student-t distribution triangular distribution uniform (rectangular) distribution von Mises distribution Weibull distribution

Functions

 • The following functions are used to retrieve information or perform another function on a probability distribution.

 compute the average absolute deviation cumulative distribution function central moments cumulant generating function characteristic function cumulants cumulant generating function cumulative distribution function deciles compute expected values hazard (failure) rate geometric mean harmonic mean hazard (failure) rate Hodges-Lehmann statistic interquartile range inverse survival function kurtosis generate a procedure for calculating statistical quantities arithmetic mean average absolute deviation from the mean median compute the median absolute deviation moment generating function Mills ratio mode moments moment generating function order statistics probability density function percentiles compute the probability of an event probability density function probability function quadratic mean quantiles quartiles create new random variables Rousseeuw and Croux' Qn Rousseeuw and Croux' Sn skewness standard deviation standard error of the sampling distribution standardized moments support set of a random variable survival function variance coefficient of variation