Empirical (FSharp.Stats)

Empirical Module

Namespace: FSharp.Stats.Distributions
Assembly: FSharp.Stats.dll

Represents a probability mass function (map from values to probabilities).

Functions and values

Function or value	Description
`add equalBandwidthOrNominal histA histB` Full Usage: `add equalBandwidthOrNominal histA histB` Parameters: equalBandwidthOrNominal : `bool` - Is the binwidth equal for both distributions? For nominal data set to true. histA : `Map<'a, ^value>` - Empirical distribution A histB : `Map<'a, ^value>` - Empirical distribution B Returns: `Map<'a, ^value>` New frequency map that results from merged maps histA and histB. Values from keys that are present in both maps are handled by f Modifiers: inline Type parameters: 'a, ^value	Merges two maps into a single map. If a key exists in both maps, the value from mapB is added to the value of mapA. When applied to continuous data the bandwidths must be equal!This function is not commutative! (add a b) is not equal to (add b a) equalBandwidthOrNominal : `bool` Is the binwidth equal for both distributions? For nominal data set to true. histA : `Map<'a, ^value>` Empirical distribution A histB : `Map<'a, ^value>` Empirical distribution B Returns: `Map<'a, ^value>` New frequency map that results from merged maps histA and histB. Values from keys that are present in both maps are handled by f
`create bandwidth data` Full Usage: `create bandwidth data` Parameters: bandwidth : `float` - data : `float seq` - Returns: `Map<float, float>`	Creates probability mass function of the input sequence. The bandwidth defines the width of the bins the numbers are sorted into. Bin intervals are half open excluding the upper border: [lower,upper) bandwidth : `float` data : `float seq` Returns: `Map<float, float>` Example
`createNominal data` Full Usage: `createNominal data` Parameters: data : `'a seq` - Returns: `Map<'a, float>` Modifiers: inline Type parameters: 'a	Creates probability mass function of the categories in the input sequence. data : `'a seq` Returns: `Map<'a, float>` Example
`createNominalWithTemplate template data` Full Usage: `createNominalWithTemplate template data` Parameters: template : `Set<'a>` - data : `'a seq` - Returns: `Map<'a, float>` Modifiers: inline Type parameters: 'a	Creates probability mass function of the categories in the input sequence. A template defines the search space to exclude certain elements or to include elements that are not in the input sequence. Frequencies are determined based only on the template set. template : `Set<'a>` data : `'a seq` Returns: `Map<'a, float>` Example
`exp pmf` Full Usage: `exp pmf` Parameters: pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Exponentiates the probabilities pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`getXValues pmf` Full Usage: `getXValues pmf` Parameters: pmf : `Map<'a, float>` - Returns: `'a seq`	Returns distinct values from pmf pmf : `Map<'a, float>` Returns: `'a seq` Example
`getYValues pmf` Full Usage: `getYValues pmf` Parameters: pmf : `Map<'a, float>` - Returns: `float seq`	Returns distinct values from pmf pmf : `Map<'a, float>` Returns: `float seq` Example
`getZip pmf` Full Usage: `getZip pmf` Parameters: pmf : `Map<'a, float>` - Returns: `('a * float) seq`	Returns: tuple of (sorted value sequence, probability sequence) pmf : `Map<'a, float>` Returns: `('a * float) seq` Example
`log pmf` Full Usage: `log pmf` Parameters: pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Log transforms the probabilities pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`maxLike pmf` Full Usage: `maxLike pmf` Parameters: pmf : `Map<'a, float>` - Returns: `float`	Returns the largest probability in the map. pmf : `Map<'a, float>` Returns: `float` Example
`mean pmf` Full Usage: `mean pmf` Parameters: pmf : `Map<float, float>` - Returns: `float`	Computes the mean of a PMF pmf : `Map<float, float>` Returns: `float` Example
`merge equalBandwidthOrNominal histA histB` Full Usage: `merge equalBandwidthOrNominal histA histB` Parameters: equalBandwidthOrNominal : `bool` - Is the binwidth equal for both distributions? For nominal data set to true. histA : `Map<'a, 'value>` - Empirical distribution A histB : `Map<'a, 'value>` - Empirical distribution B Returns: `Map<'a, 'value>` New frequency map that results from merged maps histA and histB.	Merges two maps into a single map. If a key exists in both maps, the value in histA is superseded by the value in histB. When applied to continuous data the bandwidths must be equal!This function is not commutative! (merge a b) is not equal to (merge b a) equalBandwidthOrNominal : `bool` Is the binwidth equal for both distributions? For nominal data set to true. histA : `Map<'a, 'value>` Empirical distribution A histB : `Map<'a, 'value>` Empirical distribution B Returns: `Map<'a, 'value>` New frequency map that results from merged maps histA and histB.
`mergeBy equalBandwidthOrNominal f histA histB` Full Usage: `mergeBy equalBandwidthOrNominal f histA histB` Parameters: equalBandwidthOrNominal : `bool` - Is the binwidth equal for both distributions? For nominal data set to true. f : `'value -> 'value -> 'value` - Function to transform values if key is present in both histograms. `histA-value → histB-value → newValue` histA : `Map<'a, 'value>` - Empirical distribution A histB : `Map<'a, 'value>` - Empirical distribution B Returns: `Map<'a, 'value>` New frequency map that results from merged maps mapA and mapB. Values from keys that are present in both maps are handled by f	Merges two maps into a single map. If a key exists in both maps, the value is determined by f with the first value being from mapA and the second originating from mapB. When applied to continuous data the bandwidths must be equal!This function is not commutative! (mergeBy f a b) is not equal to (mergeBy f b a) equalBandwidthOrNominal : `bool` Is the binwidth equal for both distributions? For nominal data set to true. f : `'value -> 'value -> 'value` Function to transform values if key is present in both histograms. `histA-value → histB-value → newValue` histA : `Map<'a, 'value>` Empirical distribution A histB : `Map<'a, 'value>` Empirical distribution B Returns: `Map<'a, 'value>` New frequency map that results from merged maps mapA and mapB. Values from keys that are present in both maps are handled by f
`normalize pmf` Full Usage: `normalize pmf` Parameters: pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Normalizes this PMF so the sum of all probabilities equals 1. Discrete Probability Distribution pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`normalizeBandwidth bw pmf` Full Usage: `normalizeBandwidth bw pmf` Parameters: bw : `float` - pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Normalizes this PMF by the bandwidth n/Δx Frequency Denisty Distribution bw : `float` pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`normalizePDD bw pmf` Full Usage: `normalizePDD bw pmf` Parameters: bw : `float` - pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Normalizes this PMF by the bandwidth to area equals 1. (n/N)/Δx Probability Denisty Distribution bw : `float` pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`normalizePercentage pmf` Full Usage: `normalizePercentage pmf` Parameters: pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Normalizes this PMF so the sum of all probabilities equals 100 percent Discrete Percentage Probability Distribution pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`normalizewith fraction pmf` Full Usage: `normalizewith fraction pmf` Parameters: fraction : `float` - pmf : `Map<'a, float>` - Returns: `Map<'a, float>`	Normalizes this PMF so the sum of all probabilities equals fraction fraction : `float` pmf : `Map<'a, float>` Returns: `Map<'a, float>` Example
`ofHistogram hist` Full Usage: `ofHistogram hist` Parameters: hist : `Map<'a, int>` - Returns: `Map<'a, float>`	Creates Pmf of a Histogram (normalize by n) hist : `Map<'a, int>` Returns: `Map<'a, float>` Example
`probabilities pmf` Full Usage: `probabilities pmf` Parameters: pmf : `Map<'a, float>` Returns: `float seq`	Gets an unsorted sequence of probabilities pmf : `Map<'a, float>` Returns: `float seq`
`probabilityAt pmf x` Full Usage: `probabilityAt pmf x` Parameters: pmf : `Map<'a, float>` x : `'a` Returns: `float`	Gets the probability associated with the value x pmf : `Map<'a, float>` x : `'a` Returns: `float`
`sampleFrom pmf` Full Usage: `sampleFrom pmf` Parameters: pmf : `Map<float, float>` - Returns: `float`	Chooses a random element from this PMF pmf : `Map<float, float>` Returns: `float` Example
`sum pmf` Full Usage: `sum pmf` Parameters: pmf : `Map<'a, float>` - Returns: `float`	Returns the total of the probabilities in the map pmf : `Map<'a, float>` Returns: `float` Example
`var pmf` Full Usage: `var pmf` Parameters: pmf : `Map<float, float>` - Returns: `float`	Computes the variance of a PMF pmf : `Map<float, float>` Returns: `float` Example
`varAround mu pmf` Full Usage: `varAround mu pmf` Parameters: mu : `float` - pmf : `Map<float, float>` - Returns: `float`	Computes the variance of a PMF around mu mu : `float` pmf : `Map<float, float>` Returns: `float` Example

Empirical Module

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