BetaDistribution (FsODE)

FsODE

Documentation for 0.0.2

BetaDistribution Type

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore.Redist.dll
Base Type: ContinuousDistribution

Generates Beta distributed random numbers.

The implementation of the BetaDistribution type bases upon information presented on Wikipedia - Beta distribution and Xycoon - Beta Distribution.

            
             Return Beta distributed random deviates according to the density
            
                             a-1       b-1
                            x     (1-x)
              p   (x) dx = --------------- dx   for 0 < x < 1
               a,b              B(a,b)
            
                         =  0                   otherwise
            
             References:
            
             R. C. H. Cheng, Generating Beta Variatew with Non-integral Shape
             Parameters, Comm. ACM, 21, 317-322 (1978). (Algorithms BB and BC).

/// Wikipedia - Beta distribution and Xycoon - Beta Distribution.

Constructors

Constructor Description


                
                  
                    
                      BetaDistribution()

Full Usage: BetaDistribution()

Initializes a new instance of the BetaDistribution class, using a StandardGenerator as underlying random number generator.


                
                  
                    
                      BetaDistribution(generator)

Full Usage: BetaDistribution(generator)

Parameters:

generator : Generator - A Generator object.

Initializes a new instance of the BetaDistribution class, using the specified Generator as underlying random number generator.

generator : Generator: A Generator object.

ArgumentNullException

generator is NULL ( in Visual Basic).


                
                  
                    
                      BetaDistribution(alpha, beta)

Full Usage: BetaDistribution(alpha, beta)

Parameters:

alpha : float - First parameter of the distribution.

beta : float - Second parameter of the distribution.

Initializes a new instance of the BetaDistribution class, using the specified parameters and the default Generator.

alpha : float: First parameter of the distribution.
beta : float: Second parameter of the distribution.


                
                  
                    
                      BetaDistribution(alpha, beta, generator)

Full Usage: BetaDistribution(alpha, beta, generator)

Parameters:

alpha : float - First parameter of the distribution.

beta : float - Second parameter of the distribution.

generator : Generator - A Generator object.

Initializes a new instance of the BetaDistribution class, using the specified Generator as underlying random number generator.

alpha : float: First parameter of the distribution.
beta : float: Second parameter of the distribution.
generator : Generator: A Generator object.

ArgumentNullException

generator is NULL ( in Visual Basic).

Instance members

Instance member	Description
`this.Alpha` Full Usage: `this.Alpha`	Gets or sets the parameter alpha which is used for generation of beta distributed random numbers. Call BetaDistribution.IsValidAlpha to determine whether a value is valid and therefor assignable.
`this.Beta` Full Usage: `this.Beta`	Gets or sets the parameter beta which is used for generation of beta distributed random numbers. Call BetaDistribution.IsValidBeta to determine whether a value is valid and therefor assignable.
`this.CDF` Full Usage: `this.CDF` Parameters: x : `float` Returns: `float` Modifiers: abstract	x : `float` Returns: `float`
`this.Initialize` Full Usage: `this.Initialize` Parameters: alpha : `float` beta : `float`	alpha : `float` beta : `float`
`this.IsValidAlpha` Full Usage: `this.IsValidAlpha` Parameters: value : `float` - The value to check. Returns: `bool` if value is greater than 0.0; otherwise, .	Determines whether the specified value is valid for parameter BetaDistribution.Alpha. value : `float` The value to check. Returns: `bool` if value is greater than 0.0; otherwise, .
`this.IsValidBeta` Full Usage: `this.IsValidBeta` Parameters: value : `float` - The value to check. Returns: `bool` if value is greater than 0.0; otherwise, .	Determines whether the specified value is valid for parameter BetaDistribution.Beta. value : `float` The value to check. Returns: `bool` if value is greater than 0.0; otherwise, .
`this.Maximum` Full Usage: `this.Maximum` Returns: `float` Modifiers: abstract	Gets the maximum possible value of beta distributed random numbers. Returns: `float`
`this.Mean` Full Usage: `this.Mean` Returns: `float` Modifiers: abstract	Gets the mean value of beta distributed random numbers. Returns: `float`
`this.Median` Full Usage: `this.Median` Returns: `float` Modifiers: abstract	Gets the median of beta distributed random numbers. Returns: `float`
`this.Minimum` Full Usage: `this.Minimum` Returns: `float` Modifiers: abstract	Gets the minimum possible value of beta distributed random numbers. Returns: `float`
`this.Mode` Full Usage: `this.Mode` Returns: `float[]` Modifiers: abstract	Gets the mode of beta distributed random numbers. Returns: `float[]`
`this.NextDouble` Full Usage: `this.NextDouble` Returns: `float` A beta distributed double-precision floating point number. Modifiers: abstract	Returns a beta distributed floating point random number. Returns: `float` A beta distributed double-precision floating point number.
`this.PDF` Full Usage: `this.PDF` Parameters: x : `float` Returns: `float` Modifiers: abstract	x : `float` Returns: `float`
`this.Quantile` Full Usage: `this.Quantile` Parameters: p : `float` Returns: `float` Modifiers: abstract	p : `float` Returns: `float`
`this.Variance` Full Usage: `this.Variance` Returns: `float` Modifiers: abstract	Gets the variance of beta distributed random numbers. Returns: `float`

Static members

Static member	Description
`BetaDistribution.CDF(x, A, B)` Full Usage: `BetaDistribution.CDF(x, A, B)` Parameters: x : `float` A : `float` B : `float` Returns: `float`	x : `float` A : `float` B : `float` Returns: `float`
`BetaDistribution.PDF(x, A, B)` Full Usage: `BetaDistribution.PDF(x, A, B)` Parameters: x : `float` A : `float` B : `float` Returns: `float`	x : `float` A : `float` B : `float` Returns: `float`
`BetaDistribution.Quantile(p, A, B)` Full Usage: `BetaDistribution.Quantile(p, A, B)` Parameters: p : `float` A : `float` B : `float` Returns: `float`	p : `float` A : `float` B : `float` Returns: `float`