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

Discrete Distributions

Continuous Distributions

Functions

Constructors

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

DiscreteValueMap

create a noninteger discrete distribution

Distribution

create new distribution

RandomVariable

create new random variable

Discrete Distributions

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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

Bernoulli distribution

Binomial

binomial distribution

DiscreteUniform

discrete uniform distribution

EmpiricalDistribution

empirical distribution

Geometric

geometric distribution

Hypergeometric

hypergeometric distribution

NegativeBinomial

negative binomial (Pascal) distribution

Poisson

Poisson distribution

ProbabilityTable

probability table

Continuous Distributions

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

Beta

beta distribution

Cauchy

Cauchy distribution

ChiSquare

chi-square distribution

Erlang

Erlang distribution

Error

error (exponential power) distribution

Exponential

exponential distribution

FRatio

Fisher f-distribution

Gamma

gamma distribution

Gumbel

Gumbel distribution

InverseGaussian

inverse Gaussian (Wald) distribution

Laplace

Laplace distribution

Logistic

logistic distribution

LogNormal

log normal distribution

Maxwell

Maxwell distribution

Moyal

Moyal distribution

NonCentralBeta

noncentral beta distribution

NonCentralChiSquare

noncentral chi-square distribution

NonCentralFRatio

noncentral f-distribution

NonCentralStudentT

noncentral t-distribution

Normal

normal (Gaussian) distribution

Pareto

Pareto distribution

Power

power distribution

Rayleigh

Rayleigh distribution

StudentT

Student-t distribution

Triangular

triangular distribution

Uniform

uniform (rectangular) distribution

VonMises

von Mises distribution

Weibull

Weibull distribution

Functions

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

AbsoluteDeviation

compute the average absolute deviation

CDF

cumulative distribution function

CentralMoment

central moments

CGF

cumulant generating function

CharacteristicFunction

characteristic function

Cumulant

cumulants

CumulantGeneratingFunction

cumulant generating function

CumulativeDistributionFunction

cumulative distribution function

Decile

deciles

ExpectedValue

compute expected values

FailureRate

hazard (failure) rate

GeometricMean

geometric mean

HarmonicMean

harmonic mean

HazardRate

hazard (failure) rate

HodgesLehmann

Hodges-Lehmann statistic

InterquartileRange

interquartile range

InverseSurvivalFunction

inverse survival function

Kurtosis

kurtosis

MakeProcedure

generate a procedure for calculating statistical quantities

Mean

arithmetic mean

MeanDeviation

average absolute deviation from the mean

Median

median

MedianDeviation

compute the median absolute deviation

MGF

moment generating function

MillsRatio

Mills ratio

Mode

mode

Moment

moments

MomentGeneratingFunction

moment generating function

OrderStatistic

order statistics

PDF

probability density function

Percentile

percentiles

Probability

compute the probability of an event

ProbabilityDensityFunction

probability density function

ProbabilityFunction

probability function

QuadraticMean

quadratic mean

Quantile

quantiles

Quartile

quartiles

RandomVariable

create new random variables

RousseeuwCrouxQn

Rousseeuw and Croux' Qn

RousseeuwCrouxSn

Rousseeuw and Croux' Sn

Skewness

skewness

StandardDeviation

standard deviation

StandardError

standard error of the sampling distribution

StandardizedMoment

standardized moments

Support

support set of a random variable

SurvivalFunction

survival function

Variance

variance

Variation

coefficient of variation

See Also

Statistics

Statistics[Computation]

Statistics[Simulation]