...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

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 |

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: |

quantile(cd, cr) |
RealType |
Returns the quantile (or percentile) of the distribution. |

quantile(complement(cd, cr)) |
RealType |
Returns the quantile (or percentile) of the distribution, starting
from the complement of the probability, the same as: |

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. |