LogDensity: Log Density of the GB2 Distribution

In GB2: Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation

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, θ)), where f is the GB2 density with parameters shape1 = a, scale = b, shape2 = p and shape3 = q, θ is the parameter vector. We calculate the first- and second-order partial derivatives of log(f(x, θ)) with respect to the parameter vector θ.

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.

GB2 documentation built on June 22, 2022, 9:07 a.m.