Statistics functions

Data Structures
struct	mirml_rsamp_incr_t_
	Structure for online incremental calculation of sample statistics. More...
struct	mirml_rscov_incr_t_
	Structure for online incremental calculation of covariance of two random variables. More...

Typedefs
typedef struct mirml_rsamp_incr_t_	mirml_rsamp_incr_t
	Structure for online incremental calculation of sample statistics.
typedef struct mirml_rscov_incr_t_	mirml_rscov_incr_t
	Structure for online incremental calculation of covariance of two random variables.

Functions
double	mirml_rsamp_mean (double *x, int len)
	Calculation of sample mean.
double	mirml_rsamp_mean_variance (double *x, int len, double *mean)
	Calculation of sample mean and variance.
void	mirml_rsamp_statistics4 (double *x, int len, double *mean, double *variance, double *skewness, double *kurtosis)
	Calculation of sample mean, variance, skewness and excess kurtosis.
void	mirml_rsamp_incr_init (mirml_rsamp_incr_t *rsamp)
	Initialization of online incremental calculation of sample statistics.
void	mirml_rsamp_incr_add (mirml_rsamp_incr_t *rsamp, double val)
	Add next value for online incremental calculation of sample statistics.
void	mirml_rsamp_incr_addw (mirml_rsamp_incr_t *rsamp, double val, double w)
	Add next weighted value for online incremental calculation of sample statistics. P. Pebay, T. B. Terriberry, H. Kolla, J. Bennett, Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights. Comput Stat 31, 1305–1325 (2016), 10.1007/s00180-015-0637-z.
double	mirml_rsamp_incr_pvar (mirml_rsamp_incr_t *rsamp)
	Calculate population variance.
double	mirml_rsamp_incr_svar (mirml_rsamp_incr_t *rsamp)
	Calculate sample variance using Bessel's correction.
double	mirml_rsamp_incr_rvar (mirml_rsamp_incr_t *rsamp)
	Calculate sample variance using Bessel's correction.
double	mirml_rsamp_incr_skew (mirml_rsamp_incr_t *rsamp)
	Calculate skewness.
double	mirml_rsamp_incr_kurt (mirml_rsamp_incr_t *rsamp)
	Calculate kurtosis.
void	mirml_rscov_incr_init (mirml_rscov_incr_t *csamp)
	Initialization of online incremental calculation of covariance of two random variables.
void	mirml_rscov_incr_add (mirml_rscov_incr_t *csamp, double x, double y)
	Add next value for online incremental calculation of covariance.
void	mirml_rscov_incr_addw (mirml_rscov_incr_t *csamp, double x, double y, double w)
	Add next weighted value for online incremental calculation of covariance.
double	mirml_rscov_incr_pcov (mirml_rscov_incr_t *csamp)
	Calculate population covariance, sample covariance using Bessel's correction and sample covariance in case of reliability weights.
double	mirml_rscov_incr_bcov (mirml_rscov_incr_t *csamp)
double	mirml_rscov_incr_rcov (mirml_rscov_incr_t *csamp)

Detailed Description

Function Documentation

mirml_rsamp_incr_add()

void mirml_rsamp_incr_add	(	mirml_rsamp_incr_t *	rsamp,
		double	val
	)

Add next value for online incremental calculation of sample statistics.

Note

Sample mean value is updated in this function. Variance, skewness and kurtosis can be calculated using other functions.

mirml_rsamp_incr_addw()

void mirml_rsamp_incr_addw	(	mirml_rsamp_incr_t *	rsamp,
		double	val,
		double	w
	)

Add next weighted value for online incremental calculation of sample statistics. P. Pebay, T. B. Terriberry, H. Kolla, J. Bennett, Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights. Comput Stat 31, 1305–1325 (2016), 10.1007/s00180-015-0637-z.

Note

Sample mean value is updated in this function. Variance, skewness and kurtosis can be calculated using other functions.

Warning

Do not mix weighted and unweighted incremental calculation of sample statistics.

mirml_rsamp_incr_rvar()

double mirml_rsamp_incr_rvar

(

mirml_rsamp_incr_t *

rsamp

)

Calculate sample variance using Bessel's correction.

Note

In case of weighted data, the usage of reliability weights is expected. Reliability weights: non-random values reflecting the sample's relative trustworthiness, must be normalized to unit (i.e. the sum of all weights must be equal to 1).

mirml_rsamp_incr_svar()

double mirml_rsamp_incr_svar

(

mirml_rsamp_incr_t *

rsamp

)

Calculate sample variance using Bessel's correction.

Note

In case of weighted data, frequency weights (weighting factor equals the number of occurrences) are expected.

mirml_rsamp_mean()

double mirml_rsamp_mean	(	double *	x,
		int	len
	)

Calculation of sample mean.

Parameters

[in]	x	Vector of values.
[in]	len	Length of the input vector.

Note

Implements compensated variant in http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance

Returns

Calculated mean of random sample in vector x.

mirml_rsamp_mean_variance()

double mirml_rsamp_mean_variance	(	double *	x,
		int	len,
		double *	mean
	)

Calculation of sample mean and variance.

Parameters

[in]	x	Vector of values.
[in]	len	Length of the input vector.
[out]	mean	Calculated mean if not NULL.

Note

Implements compensated variant in http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance

Returns

Calculated variance of random sample in vector x.

mirml_rsamp_statistics4()

void mirml_rsamp_statistics4	(	double *	x,
		int	len,
		double *	mean,
		double *	variance,
		double *	skewness,
		double *	kurtosis
	)

Calculation of sample mean, variance, skewness and excess kurtosis.

Parameters

[in]	x	Vector of values.
[in]	len	Length of the input vector.
[out]	mean	Calculated mean if not NULL.
[out]	mean	Calculated variance if not NULL.
[out]	mean	Calculated skewness if not NULL.
[out]	mean	Calculated excess kurtosis if not NULL.

Note

See Higher-order statistics in http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance

mirml_rscov_incr_pcov()

double mirml_rscov_incr_pcov

(

mirml_rscov_incr_t *

csamp

)

Calculate population covariance, sample covariance using Bessel's correction and sample covariance in case of reliability weights.

Note

These functions work similar to the respective functions for sample statistics. See infos there.