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

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)