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
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 non-integer discrete distribution
Distribution
create new distribution
RandomVariable
create new random variable
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 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
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
CumulativeDistributionFunction
Decile
deciles
ExpectedValue
compute expected values
FailureRate
hazard (failure) rate
GeometricMean
geometric mean
HarmonicMean
harmonic mean
HazardRate
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
OrderStatistic
order statistics
PDF
probability density function
Percentile
percentiles
Probability
compute the probability of an event
ProbabilityDensityFunction
ProbabilityFunction
probability function
QuadraticMean
quadratic mean
Quantile
quantiles
Quartile
quartiles
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]
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