Module Sample

module Sample: sig .. end

Commonly used sample statistics.

val min : float array -> float

val max : float array -> float

val minmax : float array -> float * float

val range : float array -> float

O(n) Computes sample's range, i. e. the difference between the largest and smallest elements of a sample.

val moments : int -> float array -> float array

O(n k) Computes an array of sample moments of order 1 to k, i. e. E{X^1}, E{X^2}, ..., E{X^k}.

val mean : float array -> float

O(n) Computes sample's arithmetic mean.

val variance : ?mean:float -> float array -> float

O(n) Computes unbiased estimate of a sample's variance, also known as the sample variance, where the denominator is n - 1.

val sd : ?mean:float -> float array -> float

O(n) Computes sample's standard deviation.

val skewness : ?mean:float -> ?sd:float -> float array -> float

O(n) Computes the skewness of a sample, which is a measure of asymmetry of its distribution.

val kurtosis : ?mean:float -> ?sd:float -> float array -> float

O(n) Computes the excess kurtosis of a sample, which is a measure of a "peakedness" of its distribution.

val rank : ?ties_strategy:[ `Average | `Max | `Min ] ->
       ?cmp:('a -> 'a -> int) -> 'a array -> float * float array

O(n log n) Computes sample's ranks, ties_strategy controls which ranks are assigned to equal values:

`Average the average of ranks should be assigned to each value. Default.
`Min the minimum of ranks is assigned to each value.
`Max the maximum of ranks is assigned to each value.

Returns a pair, where the first element is ties correction factor and second is an array of sample ranks.

References

P. R. Freeman, "Algorithm AS 26: Ranking an array of numbers", Vol. 19, Applied Statistics, pp111-113, 1970.

val histogram : ?n_bins:int ->
       ?range:float * float ->
       ?weights:float array ->
       ?density:bool -> float array -> float array * float array

O(n) Computes histogram of a data set. Bin sizes are uniform, based on a given range, whic defaults to (min - k, max + k), where k = (min - max) / (bins - 1) * 2. This behaviour is copied from the excellent statistics library by Brian O'Sullivan.

module Quantile: sig .. end

val quantile : ps:float array -> float array -> float array

O(n log n) Estimates sample quantile corresponding to the given probability p, using the continuous sample method with default parameters.

val iqr : float array -> float

O(n log n) Estimates interquantile range of a given sample, using the continuous sample method with given parameters.

module KDE: sig .. end

module Correlation: sig .. end

module Summary: sig .. end

Calculates summary statistics over a possibly infinite stream of data.