R: Calculates Beta function for two identical parameters,...

BetaLambdaLambda {gld} | R Documentation

## Calculates Beta function for two identical parameters, allowing non-integer negative values

### Description

By defining the Beta Function in terms of the Gamma Function,

Beta(a,b)=(Gamma(a)*Gamma(b))/Gamma(a+b)

the function can be defined for non-integer negative values of a and b. The special case of this where a=b is needed to calculate the standard errors of the L Moment estimates of the gpd type of the generalised lambda distribution, so this function carries out that calculation.

### Usage

    BetaLambdaLambda(lambda)

### Arguments

`lambda` | A vector, each element of which is used for both arguments of the Beta function.

### Details

`NaN` is returned for any negative integer elements of `lambda`.

### Value

A vector the same length as `lambda`, containing Beta(lambda,lambda)

### Author(s)

Robert King, robert.king@newcastle.edu.au, https://tolstoy.newcastle.edu.au/~rking/

Paul van Staden

### References

https://tolstoy.newcastle.edu.au/~rking/gld/

### See Also

`beta` `gamma` `fit.gpd` `GeneralisedLambdaDistribution`

### Examples

    BetaLambdaLambda(-0.3)

[Package gld version 2.6.2 Index]