SpecialFunctions

Full name Microsoft.VisualBasic.Math.Statistics.SpecialFunctions Assembly Microsoft.VisualBasic.Math.Statistics Members 24

@author Will_and_Sara

01 Syntax

Microsoft.VisualBasic.Math.Statistics.SpecialFunctions

02 Methods

Name	Overloads	Summary
Factorial	1	could be improved with unsigned integers or the gamma function
FactorialCalculation	2
Combination	1	calculates C(n, k).
Permutation	1	calculates P(n, k).
Binom	1
MutualProbability	1	http://lethalman.blogspot.com/2011/08/probability-of-union-of-independent.html
RegularizedIncompleteBetaFunction	1	The regularized incomplete beta function https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function
incbcf	1	Continued fraction expansion #1 * for incomplete beta integral
incbd	1	Continued fraction expansion #2 * for incomplete beta integral
pseries	1	Power series for incomplete beta integral.
StirlingsFormula	1	https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was stirf
EvaluatePolynomial	1	https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was polevl
IncompleteGammaComplement	1	https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was igamc
IncompleteGamma	1	https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was igam
gammaln	1	testing showed Ben's code and this code were roughly equivalent (also to excel) however, Ben's code executed faster in the time trials.
gamma	1	testing showed Ben's code and this code were roughly equivalent (also to excel) however, Ben's code executed faster in the time trials.
Covariance	1
Correlation	1
Choose	1
BinomialCoefficient	1
Binomial	1
InvBinomal	1
BetaFunction	1

03 Members

method Factorial #

Factorial(Int32, Int32)

could be improved with unsigned integers or the gamma function

Parameters

Name	Type	Description
`N`	`Int32`	-
`k`	`Int32`	-

method FactorialCalculation overload 2 #

FactorialCalculation(Int32)

Remarks

calculates n! === P(n, n).

n! = permutation(n, n)

https://en.wikipedia.org/wiki/Factorial

Parameters

Name	Type	Description
`n`	`Int32`	-

method Combination #

Combination(Int32, Int32)

calculates C(n, k).

Remarks

implements the excel function COMBIN(number, number_chosen).

COMBIN(8,2) = 28

https://en.wikipedia.org/wiki/Combination

Parameters

Name	Type	Description
`n`	`Int32`	-
`k`	`Int32`	-

method Permutation #

Permutation(Int32, Int32)

calculates P(n, k).

Remarks

https://en.wikipedia.org/wiki/Permutation

Parameters

Name	Type	Description
`n`	`Int32`	-
`k`	`Int32`	-

method Binom #

Binom(Int32, Int32)

Parameters

Name	Type	Description
`n`	`Int32`	-
`k`	`Int32`	-

method MutualProbability #

MutualProbability(Double())

http://lethalman.blogspot.com/2011/08/probability-of-union-of-independent.html

Parameters

Name	Type	Description
`probabilities`	`Double()`	-

method RegularizedIncompleteBetaFunction #

RegularizedIncompleteBetaFunction(Double, Double, Double)

The regularized incomplete beta function

https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function

Parameters

Name	Type	Description
`aa`	`Double`	-
`bb`	`Double`	-
`xx`	`Double`	-

method incbcf #

incbcf(Double, Double, Double)

Continued fraction expansion #1

for incomplete beta integral

Parameters

Name	Type	Description
`a`	`Double`	-
`b`	`Double`	-
`x`	`Double`	-

method incbd #

incbd(Double, Double, Double)

Continued fraction expansion #2

for incomplete beta integral

Parameters

Name	Type	Description
`a`	`Double`	-
`b`	`Double`	-
`x`	`Double`	-

method pseries #

pseries(Double, Double, Double)

Power series for incomplete beta integral. Use when b*x is small and x not too close to 1.

Parameters

Name	Type	Description
`a`	`Double`	-
`b`	`Double`	-
`x`	`Double`	-

method StirlingsFormula #

StirlingsFormula(Double)

https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was stirf

Parameters

Name	Type	Description
`x`	`Double`	-

method EvaluatePolynomial #

EvaluatePolynomial(Double, Double())

https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was polevl

Parameters

Name	Type	Description
`x`	`Double`	-
`coefficients`	`Double()`	-

method IncompleteGammaComplement #

IncompleteGammaComplement(Double, Double)

https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was igamc

Parameters

Name	Type	Description
`a`	`Double`	-
`x`	`Double`	-

method IncompleteGamma #

IncompleteGamma(Double, Double)

https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java //previous name was igam

Parameters

Name	Type	Description
`a`	`Double`	-
`x`	`Double`	-

method gammaln #

gammaln(Double)

testing showed Ben's code and this code were roughly equivalent (also to excel) however, Ben's code executed faster in the time trials.

Parameters

Name	Type	Description
`x`	`Double`	-

method gamma #

gamma(Double)

testing showed Ben's code and this code were roughly equivalent (also to excel) however, Ben's code executed faster in the time trials. https://www.ncnr.nist.gov/resources/sansmodels/SpecialFunction.java

Parameters

Name	Type	Description
`x`	`Double`	-

method Covariance #

Covariance(Double(), Double())

method Correlation #

Correlation(Double(), Double())

method Choose #

Choose(Int32, Int32)

method BinomialCoefficient #

BinomialCoefficient(Int32, Int32)

method FactorialCalculation #

FactorialCalculation(Int32, Int32)

method Binomial #

Binomial(Double, Int32, Int32)

method InvBinomal #

InvBinomal(Double, Int32, Int32)

method BetaFunction #

BetaFunction(Double, Double)