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

By defining the Beta Function in terms of the Gamma Function, $$B(a,b)=\frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$$ 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.

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

Robert King, robert.king.newcastle@gmail.com, https://github.com/newystats/

Paul van Staden

Examples

BetaLambdaLambda(-0.3)
#> [1] -5.064101