ProfLogLikelihood {GB2}

Profile Log-likelihood of the GB2 Distribution

Description

Expression of the parameters shape2 =p and shape3 =q of the GB2 distribution as functions of shape1 =a and scale =b, profile log-likelihood of the GB2 distribution, scores of the profile log-likelihood.

Usage

prof.gb2(x, shape1, scale, w=rep(1, length(x)))
proflogl.gb2(x, shape1, scale, w=rep(1, length(x)))
profscores.gb2(x, shape1, scale, w=rep(1, length(x)))

Arguments

x

numeric; vector of data values.

shape1

numeric; positive parameter.

scale

numeric; positive parameter.

w

numeric; vector of weights. Must have the same length as x. By default w is a vector of 1.

Details

Using the full log-likelihood equations for the GB2 distribution, the parameters p and q can be estimated as functions of a and b. These functions are plugged into the log-likelihood expression, which becomes a function of a and b only. This is obtained by reparametrizing the GB2, i.e. we set r=\frac{p}{p+q} and s=p+q. More details can be found in Graf (2009).

Value

prof returns a vector containing the values of r, s, p, q as well as two other parameters used in the calculation of the profile log-likelihood and its first derivatives. proflogl.gb2 returns the value of the profile log-likelihood and profscores.gb2 returns the vector of the first derivatives of the profile log-likelihhod with respect to a and b.

Author(s)

Monique Graf and Desislava Nedyalkova

References

Graf, M. (2009) The Log-Likelihood of the Generalized Beta Distribution of the Second Kind. working paper, SFSO.