lFTG {distTails}

FTG Log-likelihood Function

Description

This function computes the loglikelihood of the full-tail gamma with the input sample data. The expression used is:

l(x; \alpha, \sigma, \rho) = -n\left(\log\Gamma(\alpha, \rho) + \log(\sigma) -\alpha \log(\rho) - \frac{\alpha - 1}{n}\sum_{i = 1}^{n}\log\left(1 + \frac{x_{i}}{\sigma}\right) + \frac{\rho}{n} \sum_{i = 1}^{n}\left(1 + \frac{x_{i}}{\sigma}\right)\right)

Usage

lFTG(x, threshold, scale, shape)

Arguments

x

Sample data.

threshold

Minimum value of the tail.

scale

Scale parameter.

shape

Shape parameter.

Value

Gives the log-likelihood of the FTG. The length of the result is determined by the length of x.

References

del Castillo, Joan & Daoudi, Jalila & Serra, Isabel. (2012). The full-tails gamma distribution applied to model extreme values. ASTIN Bulletin. <doi:10.1017/asb.2017.9>.

Examples

lFTG(1,1,1,1)