Class UtilityFunctions

Class contains Gamma, factorial, Beta and other functions used in statistical distributions formulas.

Inheritance

System.Object

UtilityFunctions

Inherited Members

System.Object.ToString()

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.ReferenceEquals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

Namespace: Syncfusion.Windows.Forms.Chart.Statistics

Assembly: Syncfusion.Chart.Base.dll

Syntax

public static class UtilityFunctions

Methods

Beta(Double, Double)

Beta function.

Declaration

public static double Beta(double a, double b)

Parameters

Type	Name	Description
System.Double	a
System.Double	b

Returns

Type	Description
System.Double

BetaCumulativeDistribution(Double, Double, Double)

Returns cumulative beta distribution. ( for x >= 0, a > 0, b > 0 )

Declaration

public static double BetaCumulativeDistribution(double a, double b, double x)

Parameters

Type	Name	Description
System.Double	a
System.Double	b
System.Double	x

Returns

Type	Description
System.Double	Returns cumulative beta distribution. http://en.wikipedia.org/wiki/Beta_distribution) ( for x >= 0, a > 0, b > 0 )

BetaLn(Double, Double)

Logarithm of Beta function.

Declaration

public static double BetaLn(double a, double b)

Parameters

Type	Name	Description
System.Double	a
System.Double	b

Returns

Type	Description
System.Double

Binomial(Int32, Int32)

Binomial coefficient n!/(k!(n-k)!) ( for n >= k >= 0 ).

Declaration

public static double Binomial(int n, int k)

Parameters

Type	Name	Description
System.Int32	n
System.Int32	k

Returns

Type	Description
System.Double

Erf(Double)

Error function.

Declaration

public static double Erf(double x)

Parameters

Type	Name	Description
System.Double	x	.

Returns

Type	Description
System.Double	Returns error function.

Factorial(Int32)

Factorial n! ( for n >= 0 ).

Declaration

public static double Factorial(int n)

Parameters

Type	Name	Description
System.Int32	n

Returns

Type	Description
System.Double

FactorialLn(Int32)

Logarithm of factorial n! ( for n >= 0 ).

Declaration

public static double FactorialLn(int n)

Parameters

Type	Name	Description
System.Int32	n

Returns

Type	Description
System.Double

FCumulativeDistribution(Double, Double, Double)

Returns cumulative F distribution. ( for firstDegreeOfFreedom >= 1 and firstDegreeOfFreedom >= 1 )

Declaration

public static double FCumulativeDistribution(double fValue, double firstDegreeOfFreedom, double secondDegreeOfFreedom)

Parameters

Type	Name	Description
System.Double	fValue
System.Double	firstDegreeOfFreedom
System.Double	secondDegreeOfFreedom

Returns

Type	Description
System.Double	Returns T cumulative distribution. http://en.wikipedia.org/wiki/F_distribution) ( for degreeOfFreedom > 0 )

Gamma(Double)

Gamma function ( for y > 0 ).

Declaration

public static double Gamma(double y)

Parameters

Type	Name	Description
System.Double	y

Returns

Type	Description
System.Double

GammaCumulativeDistribution(Double, Double)

Returns cumulative gamma distribution. http://en.wikipedia.org/wiki/Gamma_distribution ( for x >= 0, a > 0 )

Declaration

public static double GammaCumulativeDistribution(double a, double x)

Parameters

Type	Name	Description
System.Double	a
System.Double	x

Returns

Type	Description
System.Double	Returns cumulative gamma distribution. (http://en.wikipedia.org/wiki/Gamma_distribution) ( for x >= 0, a > 0 )

GammaLn(Double)

Natural logarithm of gamma function ( for y > 0 ).

Declaration

public static double GammaLn(double y)

Parameters

Type	Name	Description
System.Double	y

Returns

Type	Description
System.Double

InverseBetaCumulativeDistribution(Double, Double, Double)

Returns inverse cumulative beta distribution. ( for 1 >= p >= 0 , a > 0, b > 0 )

Declaration

public static double InverseBetaCumulativeDistribution(double a, double b, double p)

Parameters

Type	Name	Description
System.Double	a	Beta function parameter
System.Double	b	Beta function parameter
System.Double	p	Probability

Returns

Type	Description
System.Double	Returns inverse cumulative beta distribution. http://en.wikipedia.org/wiki/Beta_distribution) ( for p in [0,1], a > 0, b > 0 )

InverseErf(Double)

Inverse Error function. This is rational approximation of erf function. The absolute value of the relative error is less than 1.15�10-9 in the entire region.

Declaration

public static double InverseErf(double x)

Parameters

Type	Name	Description
System.Double	x	value x is in (-1 , 1) range.

Returns

Type	Description
System.Double	Returns Value that corresponds to given x.

InverseFCumulativeDistribution(Double, Double, Double)

Inverse cumulative F distribution. ( for firstDegreeOfFreedom >= 1 and firstDegreeOfFreedom >= 1 )

Declaration

public static double InverseFCumulativeDistribution(double p, double firstDegreeOfFreedom, double secondDegreeOfFreedom)

Parameters

Type	Name	Description
System.Double	p	Probability (must be in range [0, 1]. )
System.Double	firstDegreeOfFreedom
System.Double	secondDegreeOfFreedom

Returns

Type	Description
System.Double	Inverse F cumulative distribution. http://en.wikipedia.org/wiki/F_distribution) ( for firstDegreeOfFreedom >= 1 and firstDegreeOfFreedom >= 1 )

InverseNormalDistribution(Double)

Inverse Normal Distribution function. This is rational approximation of Normal Distribution function. The absolute value of the relative error is less than 1.15�10-9 in the entire region. Lower tail quantile for standard normal distribution function. This function returns an approximation of the inverse cumulative standard normal distribution function. I.e., given P, it returns an approximation to the X satisfying P = Pr{Z is smaller than X} where Z is a random variable from the standard normal distribution.

Declaration

public static double InverseNormalDistribution(double p)

Parameters

Type	Name	Description
System.Double	p	Probability at which function is evaluated. p must be in ( 0,1 ) range.

Returns

Type	Description
System.Double	Returns Inverse cumulative distribution.

InverseTCumulativeDistribution(Double, Double, Boolean)

Inverse cumulative T distribution. ( for degreeOfFreedom > 0 )

Declaration

public static double InverseTCumulativeDistribution(double p, double degreeOfFreedom, bool oneTail)

Parameters

Type	Name	Description
System.Double	p	Probability (must be in range [0, 1]. )
System.Double	degreeOfFreedom
System.Boolean	oneTail

Returns

Type	Description
System.Double	Inverse T cumulative distribution. http://en.wikipedia.org/wiki/T_distribution) ( for degreeOfFreedom > 0 )

NormalDistribution(Double)

Normal Distribution function.

Declaration

public static double NormalDistribution(double x)

Parameters

Type	Name	Description
System.Double	x	Value at which the distribution is evaluated.

Returns

Type	Description
System.Double	Returns cumulative distribution. ( Returns probability that normally distributed random variable (X - mean)/sigma is smaller than x.).

NormalDistributionDensity(Double, Double, Double)

Returns Normal Distribution density function.

Declaration

public static double NormalDistributionDensity(double x, double m, double sigma)

Parameters

Type	Name	Description
System.Double	x	Value at which the distribution density is evaluated.
System.Double	m	Expected value of distribution (Mean value)
System.Double	sigma	Variance of distribution

Returns

Type	Description
System.Double

NormalDistributionDensityLn(Double, Double, Double)

Returns Logarithm of Normal Distribution density function.

Declaration

public static double NormalDistributionDensityLn(double x, double m, double sigma)

Parameters

Type	Name	Description
System.Double	x	Value at which the distribution density is evaluated.
System.Double	m	Expected value of distribution (Mean value)
System.Double	sigma	Variance of distribution

Returns

Type	Description
System.Double

TCumulativeDistribution(Double, Double, Boolean)

Returns cumulative T distribution. ( for degreeOfFreedom > 0 )

Declaration

public static double TCumulativeDistribution(double tValue, double degreeOfFreedom, bool oneTail)

Parameters

Type	Name	Description
System.Double	tValue
System.Double	degreeOfFreedom
System.Boolean	oneTail

Returns

Type	Description
System.Double	Returns T cumulative distribution. http://en.wikipedia.org/wiki/T_distribution) ( for degreeOfFreedom > 0 )