Portability | portable |
---|---|

Stability | experimental |

Maintainer | bos@serpentine.com |

Types and functions common to many probability distributions.

- class Distribution d where
- class Distribution d => Mean d where
- class Mean d => Variance d where
- findRoot :: Distribution d => d -> Double -> Double -> Double -> Double -> Double

# Documentation

class Distribution d whereSource

The interface shared by all probability distributions.

density :: d -> Double -> DoubleSource

Probability density function. The probability that a
the random variable *X* has the value *x*, i.e. P(*X*=*x*).

cumulative :: d -> Double -> DoubleSource

Cumulative distribution function. The probability that a
random variable *X* is less than *x*, i.e. P(*X*≤*x*).

quantile :: d -> Double -> DoubleSource

Inverse of the cumulative distribution function. The value
*x* for which P(*X*≤*x*).

class Distribution d => Mean d whereSource

:: Distribution d | |

=> d | |

-> Double | Probability |

-> Double | Initial guess |

-> Double | Lower bound on interval |

-> Double | Upper bound on interval |

-> Double |

Approximate the value of *X* for which P(*x*>*X*)=*p*.

This method uses a combination of Newton-Raphson iteration and
bisection with the given guess as a starting point. The upper and
lower bounds specify the interval in which the probability
distribution reaches the value *p*.