Gamma (FSharp.Stats)

Gamma Type

Namespace: FSharp.Stats.Distributions.Continuous
Assembly: FSharp.Stats.dll
Base Type: obj

 Gamma distribution
 Sampling implementation based on:
     "A Simple Method for Generating Gamma Variables" - Marsaglia & Tsang
     ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363-372.
 alpha = shape (k) 
 beta  = scale || 1 / rate (θ)

Static members

Static member	Description
`Gamma.CDF(alpha) (beta) (x)` Full Usage: `Gamma.CDF(alpha) (beta) (x)` Parameters: alpha : `float` - beta : `float` - x : `float` - Returns: `float`	Computes the cumulative distribution function. alpha : `float` beta : `float` x : `float` Returns: `float` Example
`Gamma.CheckParam(alpha) (beta)` Full Usage: `Gamma.CheckParam(alpha) (beta)` Parameters: alpha : `float` beta : `float`	alpha : `float` beta : `float`
`Gamma.Estimate(observations, ?maxIter, ?tolerance)` Full Usage: `Gamma.Estimate(observations, ?maxIter, ?tolerance)` Parameters: observations : `float[]` ?maxIter : `int` ?tolerance : `float` Returns: `ContinuousDistribution<float, float>`	Estimates a new Gamma distribution from a given set of observations. observations : `float[]` ?maxIter : `int` ?tolerance : `float` Returns: `ContinuousDistribution<float, float>`
`Gamma.Fit(observations, ?maxIter, ?tolerance)` Full Usage: `Gamma.Fit(observations, ?maxIter, ?tolerance)` Parameters: observations : `float[]` ?maxIter : `int` ?tolerance : `float` Returns: `float * float`	Fits the underlying distribution to a given set of observations. observations : `float[]` ?maxIter : `int` ?tolerance : `float` Returns: `float * float`
`Gamma.FromMean(alpha) (mean)` Full Usage: `Gamma.FromMean(alpha) (mean)` Parameters: alpha : `float` - mean : `float` - Returns: `ContinuousDistribution<float, float>`	Initializes a Gamma distribution alpha = shape (k) beta = scale \|\| 1 / rate (θ) alpha : `float` mean : `float` Returns: `ContinuousDistribution<float, float>` Example
`Gamma.FromRate(shape) (rate)` Full Usage: `Gamma.FromRate(shape) (rate)` Parameters: shape : `float` - rate : `float` - Returns: `ContinuousDistribution<float, float>`	Initializes a Gamma distribution alpha = shape (k) beta = scale \|\| 1 / rate (θ) shape : `float` rate : `float` Returns: `ContinuousDistribution<float, float>` Example
`Gamma.Init(alpha) (beta)` Full Usage: `Gamma.Init(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `ContinuousDistribution<float, float>`	Initializes a Gamma distribution alpha = shape (k) beta = scale \|\| 1 / rate (θ) alpha : `float` beta : `float` Returns: `ContinuousDistribution<float, float>` Example
`Gamma.InvCDF(alpha) (beta) (p)` Full Usage: `Gamma.InvCDF(alpha) (beta) (p)` Parameters: alpha : `float` - Shape parameter α (must be > 0). beta : `float` - Rate parameter β (must be > 0). p : `float` - Cumulative probability in [0, 1]. Returns: `float` The quantile value x such that P(X ≤ x) = p.	Inverse CDF (quantile function) for the Gamma(α, β) distribution. Uses tail-recursive Newton-Raphson refinement alpha : `float` Shape parameter α (must be > 0). beta : `float` Rate parameter β (must be > 0). p : `float` Cumulative probability in [0, 1]. Returns: `float` The quantile value x such that P(X ≤ x) = p.
`Gamma.Mean(alpha) (beta)` Full Usage: `Gamma.Mean(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `float`	Computes the mean. alpha : `float` beta : `float` Returns: `float` Example
`Gamma.Mode(alpha) (beta)` Full Usage: `Gamma.Mode(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `float`	Computes the mode. alpha : `float` beta : `float` Returns: `float` Example
`Gamma.PDF(alpha) (beta) (x)` Full Usage: `Gamma.PDF(alpha) (beta) (x)` Parameters: alpha : `float` - beta : `float` - x : `float` - Returns: `float`	Computes the probability density function. alpha : `float` beta : `float` x : `float` Returns: `float` Example
`Gamma.PDFLn(alpha) (beta) (x)` Full Usage: `Gamma.PDFLn(alpha) (beta) (x)` Parameters: alpha : `float` - beta : `float` - x : `float` - Returns: `float`	Computes the log probability density function. alpha : `float` beta : `float` x : `float` Returns: `float` Example
`Gamma.Sample(alpha) (beta)` Full Usage: `Gamma.Sample(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `float`	Produces a random sample using the current random number generator (from GetSampleGenerator()). alpha : `float` beta : `float` Returns: `float` Example
`Gamma.SampleUnchecked(alpha) (beta)` Full Usage: `Gamma.SampleUnchecked(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `float`	Produces a random sample using the current random number generator (from GetSampleGenerator()). alpha : `float` beta : `float` Returns: `float` Example
`Gamma.StandardDeviation(alpha) (beta)` Full Usage: `Gamma.StandardDeviation(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `float`	Computes the standard deviation. alpha : `float` beta : `float` Returns: `float` Example
`Gamma.Support(alpha) (beta)` Full Usage: `Gamma.Support(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `Interval<float>`	Returns the support of the gamma distribution: [0, Positive Infinity). alpha : `float` beta : `float` Returns: `Interval<float>` Example
`Gamma.ToString(alpha) (beta)` Full Usage: `Gamma.ToString(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `string`	A string representation of the distribution. alpha : `float` beta : `float` Returns: `string` Example
`Gamma.Variance(alpha) (beta)` Full Usage: `Gamma.Variance(alpha) (beta)` Parameters: alpha : `float` - beta : `float` - Returns: `float`	Computes the variance. alpha : `float` beta : `float` Returns: `float` Example

Gamma Type

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