BetaLambdaLambda

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.

math

The generalised lambda distribution, or Tukey lambda distribution,
provides a wide variety of shapes with one functional form.
This package provides random numbers, quantiles, probabilities,
densities and density quantiles for four different types of the distribution,
the FKML (Freimer et al 1988), RS (Ramberg and Schmeiser 1974), GPD (van Staden
and Loots 2009) and FM5 - see documentation for details.
It provides the density function, distribution function, and Quantile-Quantile
plots.
It implements a variety of estimation methods for the distribution,
including diagnostic plots.
Estimation methods include the starship (all 4 types),
method of L-Moments for the GPD and FKML types, and a
number of methods for only the FKML type.
These include maximum likelihood, maximum product of spacings,
Titterington's method, Moments, Trimmed L-Moments and
Distributional Least Absolutes.

Robert King

Estimation and Use of the Generalised (Tukey) Lambda
Distribution

Benjamin Dean

Sigbert Klinke

Paul van Staden

BetaLambdaLambda function

<dl> <dt>lambda</dt>
<dd>A vector, each element of which is used for both 
 arguments of the Beta function.</dd></dl>

Arguments

Robert King, <a href="/link/robert.king.newcastle%40gmail.com?package=gld&version=2.6.7" data-mini-rdoc="gld::robert.king.newcastle@gmail.com">robert.king.newcastle@gmail.com</a>, <a href="https://github.com/newystats/">https://github.com/newystats/</a>
Paul van Staden

Author

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

<dl>

 <dt>lambda</dt>
<dd>A vector, each element of which is used for both 
 arguments of the Beta function.</dd>

</dl>

Robert King, <a href='mailto:robert.king.newcastle@gmail.com'>robert.king.newcastle@gmail.com</a>, <a href='https://github.com/newystats/'>https://github.com/newystats/</a>
Paul van Staden

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

Description

Usage

Value

Arguments

Author

Details

References

See Also

Examples