lFTG: FTG Log-likelihood Function

In SergiVilardell/distributionTails: A Collection of Full Defined Distribution Tails

Description

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

l(x; α, σ, ρ) = -n≤ft(\logΓ(α, ρ) + \log(σ) -α \log(ρ) - \frac{α - 1}{n}∑_{i = 1}^{n}\log≤ft(1 + \frac{x_{i}}{σ}\right) + \frac{ρ}{n} ∑_{i = 1}^{n}≤ft(1 + \frac{x_{i}}{σ}\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)

SergiVilardell/distributionTails documentation built on Jan. 17, 2021, 8:44 a.m.