Categorical (FSharp.Stats) | FSharp.Stats

FSharp.Stats

Categorical Type

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

Categorical distribution (finite discrete distribution over k categories with probabilities).

Static members

Static member	Description
`Categorical.CDF(probabilities) (x)` Full Usage: `Categorical.CDF(probabilities) (x)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. x : `float` - A float value where CDF is evaluated (interpreted as an index). Returns: `float` The cumulative probability up to and including ⌊x⌋.	Computes the cumulative distribution function at x: P(X ≤ x). probabilities : `float[]` An array of probabilities over k categories. x : `float` A float value where CDF is evaluated (interpreted as an index). Returns: `float` The cumulative probability up to and including ⌊x⌋.
`Categorical.CdfToPmf(cdf)` Full Usage: `Categorical.CdfToPmf(cdf)` Parameters: cdf : `float[]` - An array of cumulative weights. Returns: `float array` A normalized probability mass function.	Converts a cumulative unnormalized weight array into a normalized PMF. cdf : `float[]` An array of cumulative weights. Returns: `float array` A normalized probability mass function.
`Categorical.CheckParam(probabilities)` Full Usage: `Categorical.CheckParam(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories.	Checks if the given probability vector is valid (all values ∈ [0,1] and sum to 1). probabilities : `float[]` An array of probabilities over k categories.
`Categorical.Estimate(numCategories) (observations)` Full Usage: `Categorical.Estimate(numCategories) (observations)` Parameters: numCategories : `int` - Total number of categories. observations : `int[]` - Array of category indices (0-based). Returns: `DiscreteDistribution<float, int>` A categorical distribution fitted to the observations.	Estimates a categorical distribution from observed category indices. numCategories : `int` Total number of categories. observations : `int[]` Array of category indices (0-based). Returns: `DiscreteDistribution<float, int>` A categorical distribution fitted to the observations.
`Categorical.Fit(numCategories) (observations)` Full Usage: `Categorical.Fit(numCategories) (observations)` Parameters: numCategories : `int` - Total number of categories. observations : `int[]` - Array of category indices (0-based). Returns: `float array` Estimated probability vector.	Fits the categorical distribution to a set of integer observations (category indices). numCategories : `int` Total number of categories. observations : `int[]` Array of category indices (0-based). Returns: `float array` Estimated probability vector.
`Categorical.FromCdfUnnormalized(cdf)` Full Usage: `Categorical.FromCdfUnnormalized(cdf)` Parameters: cdf : `float[]` - An array of cumulative unnormalized weights. Returns: `DiscreteDistribution<float, int>` A normalized Categorical distribution.	Initializes a Categorical distribution from an unnormalized CDF. cdf : `float[]` An array of cumulative unnormalized weights. Returns: `DiscreteDistribution<float, int>` A normalized Categorical distribution.
`Categorical.Init(probabilities)` Full Usage: `Categorical.Init(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `DiscreteDistribution<float, int>` A distribution implementing DiscreteDistribution.	Initializes a categorical distribution instance from a given probability vector. probabilities : `float[]` An array of probabilities over k categories. Returns: `DiscreteDistribution<float, int>` A distribution implementing DiscreteDistribution.
`Categorical.Mean(probabilities)` Full Usage: `Categorical.Mean(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `float` The weighted average of indices based on probabilities.	Computes the mean (expected index) of the categorical distribution. probabilities : `float[]` An array of probabilities over k categories. Returns: `float` The weighted average of indices based on probabilities.
`Categorical.PMF(probabilities) (k)` Full Usage: `Categorical.PMF(probabilities) (k)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. k : `int` - The index to evaluate. Returns: `float` The probability of observing category k.	Computes the probability mass function at index k: P(X = k). probabilities : `float[]` An array of probabilities over k categories. k : `int` The index to evaluate. Returns: `float` The probability of observing category k.
`Categorical.Sample(probabilities)` Full Usage: `Categorical.Sample(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `int` An integer representing the sampled category index.	Generates a random sample from the categorical distribution. probabilities : `float[]` An array of probabilities over k categories. Returns: `int` An integer representing the sampled category index.
`Categorical.SampleUnchecked(probabilities)` Full Usage: `Categorical.SampleUnchecked(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `int` An integer representing the sampled category index.	Generates a random sample from the categorical distribution. No parameter checking. probabilities : `float[]` An array of probabilities over k categories. Returns: `int` An integer representing the sampled category index.
`Categorical.Support(probabilities)` Full Usage: `Categorical.Support(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `Interval<int>` A closed interval [0, k-1].	Returns the support (valid outcome range) of the distribution: [0, k-1]. probabilities : `float[]` An array of probabilities over k categories. Returns: `Interval<int>` A closed interval [0, k-1].
`Categorical.ToString(probabilities)` Full Usage: `Categorical.ToString(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `string` A string describing the distribution.	Returns a string representation of the categorical distribution. probabilities : `float[]` An array of probabilities over k categories. Returns: `string` A string describing the distribution.
`Categorical.Variance(probabilities)` Full Usage: `Categorical.Variance(probabilities)` Parameters: probabilities : `float[]` - An array of probabilities over k categories. Returns: `float` The variance: E[X²] - (E[X])².	Computes the variance of the categorical distribution. probabilities : `float[]` An array of probabilities over k categories. Returns: `float` The variance: E[X²] - (E[X])².