LogDensity {GB2}

Log Density of the GB2 Distribution

Description

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.

Usage

logf.gb2(x, shape1, scale, shape2, shape3)
dlogf.gb2(xi, shape1, scale, shape2, shape3)
d2logf.gb2(xi, shape1, scale, shape2, shape3)

Arguments

xi

numeric; a data value.

x

numeric; a vector of data values.

shape1

numeric; positive parameter.

scale

numeric; positive parameter.

shape2, shape3

numeric; positive parameters of the Beta distribution.

Details

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.

Value

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.

Author(s)

Desislava Nedyalkova

References

Brazauskas, V. (2002) Fisher information matrix for the Feller-Pareto distribution. Statistics & Probability Letters, 59, 159–167.