API of the normal distribution. More...

#include "clProbDist/clProbDist.h"
#include "clProbDist/continuous.h"

Typedefs
typedef struct _clprobdistNormal	clprobdistNormal
	Normal distribution object [device]. More...

Functions
Functions for standard normal distribution
These functions are for the normal distribution with \(\mu = 0\) and \(\sigma = 1\), and they take neither a distribution object nor a list of distribution parameters.
cl_double	clprobdistStdNormalDensity (cl_double x, clprobdistStatus *err)
	Probability density function [device]. More...

cl_double	clprobdistStdNormalCDF (cl_double x, clprobdistStatus *err)
	Cumulative density function [device]. More...

cl_double	clprobdistStdNormalComplCDF (cl_double x, clprobdistStatus *err)
	Complementary CDF or reliability function [device]. More...

cl_double	clprobdistStdNormalInverseCDF (cl_double u, clprobdistStatus *err)
	Inverse cumulative density function [device]. More...

Functions to create and destroy distribution objects
clprobdistNormal *	clprobdistNormalCreate (cl_double mu, cl_double sigma, size_t bufSize, clprobdistStatus err)
	Create a distribution object. More...

clprobdistStatus	clprobdistNormalDestroy (clprobdistNormal *dist)
	Destroy a distribution object. More...

Functions for use with a distribution object
cl_double	clprobdistNormalDensityWithObject (const clprobdistNormal dist, cl_double x, clprobdistStatus err)
	Probability density function [device]. More...

cl_double	clprobdistNormalCDFWithObject (const clprobdistNormal dist, cl_double x, clprobdistStatus err)
	Cumulative density function [device]. More...

cl_double	clprobdistNormalComplCDFWithObject (const clprobdistNormal dist, cl_double x, clprobdistStatus err)
	Complementary CDF or reliability function [device]. More...

cl_double	clprobdistNormalInverseCDFWithObject (const clprobdistNormal dist, cl_double u, clprobdistStatus err)
	Inverse cumulative density function [device]. More...

cl_double	clprobdistNormalMeanWithObject (const clprobdistNormal dist, clprobdistStatus err)
	Mean of the distribution [device]. More...

cl_double	clprobdistNormalVarianceWithObject (const clprobdistNormal dist, clprobdistStatus err)
	Variance of the distribution [device]. More...

cl_double	clprobdistNormalStdDeviationWithObject (const clprobdistNormal dist, clprobdistStatus err)
	Standard deviation of the distribution [device]. More...

cl_double	clprobdistNormalGetMu (const clprobdistNormal dist, clprobdistStatus err)
	Return the mean. More...

cl_double	clprobdistNormalGetSigma (const clprobdistNormal dist, clprobdistStatus err)
	Return the standard deviation. More...

Functions for use with explicit distribution parameters
cl_double	clprobdistNormalDensity (cl_double mu, cl_double sigma, cl_double x, clprobdistStatus *err)
	Probability density function [device]. More...

cl_double	clprobdistNormalCDF (cl_double mu, cl_double sigma, cl_double x, clprobdistStatus *err)
	Cumulative density function [device]. More...

cl_double	clprobdistNormalComplCDF (cl_double mu, cl_double sigma, cl_double x, clprobdistStatus *err)
	Complementary CDF or reliability function [device]. More...

cl_double	clprobdistNormalInverseCDF (cl_double mu, cl_double sigma, cl_double u, clprobdistStatus *err)
	Inverse cumulative density function [device]. More...

cl_double	clprobdistNormalMean (cl_double mu, cl_double sigma, clprobdistStatus *err)
	Mean of the distribution [device]. More...

cl_double	clprobdistNormalVariance (cl_double mu, cl_double sigma, clprobdistStatus *err)
	Variance of the distribution [device]. More...

cl_double	clprobdistNormalStdDeviation (cl_double mu, cl_double sigma, clprobdistStatus *err)
	Standard deviation of the distribution [device]. More...

Detailed Description

API of the normal distribution.

Implementation of clProbDist_template.h for the normal distribution, adapted from [5] .

Typedef Documentation

typedef struct _clprobdistNormal clprobdistNormal

Normal distribution object [device].

A structure that represents a normal distribution object.

Function Documentation

cl_double clprobdistStdNormalDensity	(	cl_double	x,
		clprobdistStatus *	err
	)

Probability density function [device].

Same as clprobdistDensityWithObject(), but with explicit distribution parameters instead of distribution object.

This function is defined only for continuous distributions (see Implemented distributions).

See Implemented distributions for the expansion of DIST_PARAMS.

Parameters

[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(f(x)\).

cl_double clprobdistStdNormalCDF	(	cl_double	x,
		clprobdistStatus *	err
	)

Cumulative density function [device].

Same as clprobdistCDFWithObject(), but with explicit distribution parameters instead of distribution object.

See Implemented distributions for the expansion of DIST_PARAMS.

Parameters

[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(F(x)\).

cl_double clprobdistStdNormalComplCDF	(	cl_double	x,
		clprobdistStatus *	err
	)

Complementary CDF or reliability function [device].

Same as clprobdistComplCDFWithObject(), but with explicit distribution parameters instead of distribution object.

See Implemented distributions for the expansion of DIST_PARAMS.

Parameters

[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(\bar F(x)\).

cl_double clprobdistStdNormalInverseCDF	(	cl_double	u,
		clprobdistStatus *	err
	)

Inverse cumulative density function [device].

Same as clprobdistInverseCDFWithObject(), but with explicit distribution parameters instead of distribution object.

See Implemented distributions for the expansion of DIST_PARAMS.

Parameters

[in]	u	Value of \(u \in [0,1]\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(F^{-1}(u)\).

clprobdistNormal* clprobdistNormalCreate	(	cl_double	mu,
		cl_double	sigma,
		size_t *	bufSize,
		clprobdistStatus *	err
	)

Create a distribution object.

Create a new normal distribution object. Since this function allocates memory for the new distribution object; clprobdistDestroy() must be called to release the allocated memory.

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[out]	bufSize	Size in bytes of the created distribution object, or `NULL`.
[out]	err	Error status variable, or `NULL`.

Returns: New distribution object.

clprobdistStatus clprobdistNormalDestroy ( clprobdistNormal * dist )

Destroy a distribution object.

Release the resources associated to a distribution object.

Parameters

[in,out] dist Distribution object.

Returns: Error status.

cl_double clprobdistNormalDensityWithObject	(	const clprobdistNormal *	dist,
		cl_double	x,
		clprobdistStatus *	err
	)

Probability density function [device].

Return \(f(x)\), the value at \(x=\)x of the probability density function associated with the distribution object dist.

This function is defined only for continuous distributions (see Implemented distributions).

Parameters

[in]	dist	Distribution object.
[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(f(x)\).

cl_double clprobdistNormalCDFWithObject	(	const clprobdistNormal *	dist,
		cl_double	x,
		clprobdistStatus *	err
	)

Cumulative density function [device].

Return \(F(x)\), the value at \(x=\)x of the distribution function associated with the distribution object dist.

Parameters

[in]	dist	Distribution object.
[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(F(x)\).

cl_double clprobdistNormalComplCDFWithObject	(	const clprobdistNormal *	dist,
		cl_double	x,
		clprobdistStatus *	err
	)

Complementary CDF or reliability function [device].

Return \(\bar F(x)\), the value of the complementary distribution function associated with the distribution object dist.

Parameters

[in]	dist	Distribution object.
[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(\bar F(x)\).

cl_double clprobdistNormalInverseCDFWithObject	(	const clprobdistNormal *	dist,
		cl_double	u,
		clprobdistStatus *	err
	)

Inverse cumulative density function [device].

Return \(F^{-1}(u)\), the value at \(u=\)u of the inverse distribution function associated with the distribution object dist. The type of the return value is cl_int for a discrete distribution of cl_double for a continuous distribution.

Parameters

[in]	dist	Distribution object.
[in]	u	Value of \(u \in [0,1]\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(F^{-1}(u)\).

cl_double clprobdistNormalMeanWithObject	(	const clprobdistNormal *	dist,
		clprobdistStatus *	err
	)

Mean of the distribution [device].

Return the mean of the distribution associated with the distribution object dist.

Parameters

[in]	dist	Distribution object.
[out]	err	Error status variable, or `NULL`.

Returns: Mean of the distribution.

cl_double clprobdistNormalVarianceWithObject	(	const clprobdistNormal *	dist,
		clprobdistStatus *	err
	)

Variance of the distribution [device].

Return the variance of the distribution associated with the distribution object dist.

Parameters

[in]	dist	Distribution object.
[out]	err	Error status variable, or `NULL`.

Returns: Variance of the distribution.

cl_double clprobdistNormalStdDeviationWithObject	(	const clprobdistNormal *	dist,
		clprobdistStatus *	err
	)

Standard deviation of the distribution [device].

Return the standard deviation of the distribution associated with the distribution object dist.

Parameters

[in]	dist	Distribution object.
[out]	err	Error status variable, or `NULL`.

Returns: Standard deviation of the distribution.

cl_double clprobdistNormalGetMu	(	const clprobdistNormal *	dist,
		clprobdistStatus *	err
	)

Return the mean.

Parameters

[in]	dist	Distribution object.
[out]	err	Error status variable, or `NULL`.

Returns: Mean \(\mu\).

cl_double clprobdistNormalGetSigma	(	const clprobdistNormal *	dist,
		clprobdistStatus *	err
	)

Return the standard deviation.

Parameters

[in]	dist	Distribution object.
[out]	err	Error status variable, or `NULL`.

Returns: Standard deviation \(\sigma\).

cl_double clprobdistNormalDensity	(	cl_double	mu,
		cl_double	sigma,
		cl_double	x,
		clprobdistStatus *	err
	)

Probability density function [device].

See also: clprobdistNormalDensityWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(f(x)\).

cl_double clprobdistNormalCDF	(	cl_double	mu,
		cl_double	sigma,
		cl_double	x,
		clprobdistStatus *	err
	)

Cumulative density function [device].

See also: clprobdistNormalCDFWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(F(x)\).

cl_double clprobdistNormalComplCDF	(	cl_double	mu,
		cl_double	sigma,
		cl_double	x,
		clprobdistStatus *	err
	)

Complementary CDF or reliability function [device].

See also: clprobdistNormalComplCDFWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[in]	x	Value of \(x\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(\bar F(x)\).

cl_double clprobdistNormalInverseCDF	(	cl_double	mu,
		cl_double	sigma,
		cl_double	u,
		clprobdistStatus *	err
	)

Inverse cumulative density function [device].

See also: clprobdistNormalInverseCDFWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[in]	u	Value of \(u \in [0,1]\).
[out]	err	Error status variable, or `NULL`.

Returns: Value of \(F^{-1}(u)\).

cl_double clprobdistNormalMean	(	cl_double	mu,
		cl_double	sigma,
		clprobdistStatus *	err
	)

Mean of the distribution [device].

See also: clprobdistNormalMeanWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[out]	err	Error status variable, or `NULL`.

Returns: Mean of the distribution.

cl_double clprobdistNormalVariance	(	cl_double	mu,
		cl_double	sigma,
		clprobdistStatus *	err
	)

Variance of the distribution [device].

See also: clprobdistNormalVarianceWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[out]	err	Error status variable, or `NULL`.

Returns: Variance of the distribution.

cl_double clprobdistNormalStdDeviation	(	cl_double	mu,
		cl_double	sigma,
		clprobdistStatus *	err
	)

Standard deviation of the distribution [device].

See also: clprobdistNormalStdDeviationWithObject()

Parameters

[in]	mu	Value of the mean \(\mu\).
[in]	sigma	Value of the standard deviation \(\sigma\).
[out]	err	Error status variable, or `NULL`.

Returns: Standard deviation of the distribution.

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation