Calculates the log density of the GB2 distribution for a single value or a vector of values. Calculates the first- and second-order partial derivatives of the log density evaluated at a single value.
logf.gb2(x, shape1, scale, shape2, shape3)
dlogf.gb2(xi, shape1, scale, shape2, shape3)
d2logf.gb2(xi, shape1, scale, shape2, shape3)numeric; a data value.
numeric; a vector of data values.
numeric; positive parameter.
numeric; positive parameter.
numeric; positive parameters of the Beta distribution.
Depending on the input logf.gb2 gives the log density for a single value or a vector of values. dlogf.gb2 gives the vector of the four first-order partial derivatives of the log density and
d2logf.gb2 gives the \(4 \times 4\) matrix of second-order partial derivatives of the log density.
We calculate \(log(f(x, \theta))\), where \(f\) is the GB2 density with parameters shape1 \(= a\), scale \(= b\),
shape2 \(= p\) and shape3 \(= q\), \(\theta\) is the parameter vector. We calculate the first- and second-order partial derivatives of \(log(f(x, \theta))\) with
respect to the parameter vector \(\theta\).
Brazauskas, V. (2002) Fisher information matrix for the Feller-Pareto distribution. Statistics & Probability Letters, 59, 159--167.