Distribution

Full name Microsoft.VisualBasic.Math.Statistics.Distributions.Distribution Assembly Microsoft.VisualBasic.Math.Statistics Members 21

01 Syntax

Microsoft.VisualBasic.Math.Statistics.Distributions.Distribution

02 Methods

Name	Overloads	Summary
Ex	1	The ex method takes a double x as an input, if x is less than -BIGX it returns 0, otherwise it returns Euler's number e raised to the power of x.
Beta	1	The beta method takes a double {@link java.lang.reflect.Array} x as an input.
GammaLn	1	The gammaLn method takes a double x as an input and returns the logarithmic result of the gamma distribution at point x.
ZNormal	1	The zNormal method performs the Z-Normalization.
ZInverse	1	the zInverse method returns the Z-Inverse of given probability value.
ChiSquare	1	The chiSquare method is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.
ChiSquareInverse	1	The chiSquareInverse method returns the Chi Square-Inverse of given probability value with given degree of freedom.
FDistribution	1	The f-Distribution method is used to observe whether two samples have the same variance.
FDistributionInverse	1	The fDistributionInverse method returns the F-Distribution Inverse of given probability value.
TDistribution	1	The tDistribution method is used instead of the normal distribution when there is small samples.
TDistributionInverse	1	The tDistributionInverse method returns the T-Distribution Inverse of given probability value.

03 Fields

Name	Overloads	Summary
Z_MAX	1
Z_EPSILON	1
CHI_EPSILON	1
CHI_MAX	1
LOG_SQRT_PI	1
I_SQRT_PI	1
BIGX	1
I_PI	1
F_EPSILON	1
F_MAX	1

04 Members

method Ex #

Ex(Double)

The ex method takes a double x as an input, if x is less than -BIGX it returns 0, otherwise it returns Euler's number e raised to the power of x.

Parameters

Name	Type	Description
`x`	`Double`	-

Returns

0 if input is less than -BIGX, Euler's number e raised to the power of x otherwise.

method Beta #

Beta(Double())

The beta method takes a double {@link java.lang.reflect.Array} x as an input. It loops through x and accumulates the value of gammaLn(x), also it sums up the items of x and returns (accumulated result - gammaLn of this summation).

Parameters

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

Returns

gammaLn(sum).

method GammaLn #

GammaLn(Double)

The gammaLn method takes a double x as an input and returns the logarithmic result of the gamma distribution at point x.

Parameters

Name	Type	Description
`x`	`Double`	-

Returns

the logarithmic result of the gamma distribution at point x.

method ZNormal #

ZNormal(Double)

The zNormal method performs the Z-Normalization. It ensures, that all elements of the input vector are transformed into the output vector whose mean is approximately 0 while the standard deviation is in a range close to 1.

Parameters

Name	Type	Description
`z`	`Double`	-

Returns

normalized value of given input.

method ZInverse #

ZInverse(Double)

the zInverse method returns the Z-Inverse of given probability value.

Parameters

Name	Type	Description
`p`	`Double`	double probability.

Returns

the Z-Inverse of given probability.

method ChiSquare #

ChiSquare(Double, Int32)

The chiSquare method is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It takes a double input x and an integer freedom for degrees of freedom as inputs. It returns the Chi Squared result.

Parameters

Name	Type	Description
`x`	`Double`	a numeric input.
`freedom`	`Int32`	integer input for degrees of freedom.

Returns

the Chi Squared result.

method ChiSquareInverse #

ChiSquareInverse(Double, Int32)

The chiSquareInverse method returns the Chi Square-Inverse of given probability value with given degree of freedom.

Parameters

Name	Type	Description
`p`	`Double`	double probability.
`freedom`	`Int32`	integer input for degrees of freedom.

Returns

the chiSquare-Inverse of given probability.

method FDistribution #

FDistribution(Double, Int32, Int32)

The f-Distribution method is used to observe whether two samples have the same variance. It takes a double input F and two integer freedom1 and freedom2 for degrees of freedom as inputs. It returns the F-Distribution result.

Parameters

Name	Type	Description
`fValue`	`Double`	-
`freedom1`	`Int32`	integer input for degrees of freedom.
`freedom2`	`Int32`	integer input for degrees of freedom.

Returns

the F-Distribution result.

method FDistributionInverse #

FDistributionInverse(Double, Int32, Int32)

The fDistributionInverse method returns the F-Distribution Inverse of given probability value.

Parameters

Name	Type	Description
`p`	`Double`	double probability.
`freedom1`	`Int32`	integer input for degrees of freedom.
`freedom2`	`Int32`	integer input for degrees of freedom.

Returns

the F-Distribution Inverse of given probability.

method TDistribution #

TDistribution(Double, Int32)

The tDistribution method is used instead of the normal distribution when there is small samples. It takes a double input T and an integer freedom for degree of freedom as inputs. It returns the T-Distribution result by using F-Distribution method.

Parameters

Name	Type	Description
`T`	`Double`	-
`freedom`	`Int32`	integer input for degrees of freedom.

Returns

the T-Distribution result.

method TDistributionInverse #

TDistributionInverse(Double, Int32)

The tDistributionInverse method returns the T-Distribution Inverse of given probability value.

Parameters

Name	Type	Description
`p`	`Double`	double probability.
`freedom`	`Int32`	integer input for degrees of freedom.

Returns

the T-Distribution Inverse of given probability.

field Z_MAX #

Z_MAX

field Z_EPSILON #

Z_EPSILON

field CHI_EPSILON #

CHI_EPSILON

field CHI_MAX #

CHI_MAX

field LOG_SQRT_PI #

LOG_SQRT_PI

field I_SQRT_PI #

I_SQRT_PI

field BIGX #

BIGX

field I_PI #

I_PI

field F_EPSILON #

F_EPSILON

field F_MAX #

F_MAX