ProfLogLikelihood | R Documentation |
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.
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)))
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 |
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).
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.
Monique Graf and Desislava Nedyalkova
Graf, M. (2009) The Log-Likelihood of the Generalized Beta Distribution of the Second Kind. working paper, SFSO.
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