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Conceptual Requirements for Distribution Types

A DistributionType is a type that implements the following conceptual requirements, and encapsulates a statistical distribution.

Please note that this documentation should not be used as a substitute for the reference documentation, and tutorial of the statistical distributions.

In the following table, d is an object of type DistributionType, cd is an object of type const DistributionType and cr is an object of a type convertible to RealType.

Expression

Result Type

Notes

DistributionType::value_type

RealType

The real-number type RealType upon which the distribution operates.

DistributionType::policy_type

RealType

The Policy to use when evaluating functions that depend on this distribution.

d = cd

Distribution&

Distribution types are assignable.

Distribution(cd)

Distribution

Distribution types are copy constructible.

pdf(cd, cr)

RealType

Returns the PDF of the distribution.

cdf(cd, cr)

RealType

Returns the CDF of the distribution.

cdf(complement(cd, cr))

RealType

Returns the complement of the CDF of the distribution, the same as: 1-cdf(cd, cr)

quantile(cd, cr)

RealType

Returns the quantile of the distribution.

quantile(complement(cd, cr))

RealType

Returns the quantile of the distribution, starting from the complement of the probability, the same as: quantile(cd, 1-cr)

chf(cd, cr)

RealType

Returns the cumulative hazard function of the distribution.

hazard(cd, cr)

RealType

Returns the hazard function of the distribution.

kurtosis(cd)

RealType

Returns the kurtosis of the distribution.

kurtosis_excess(cd)

RealType

Returns the kurtosis excess of the distribution.

mean(cd)

RealType

Returns the mean of the distribution.

mode(cd)

RealType

Returns the mode of the distribution.

skewness(cd)

RealType

Returns the skewness of the distribution.

standard_deviation(cd)

RealType

Returns the standard deviation of the distribution.

variance(cd)

RealType

Returns the variance of the distribution.


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