This function computes the probability of the full-tail gamma with the input sample data. The expression for the probability used is:
$$G(x; \alpha, \theta, \rho) = 1 - \Gamma\left(\alpha, \rho\left(1 + \frac{x}{\sigma}\right)\right)/\Gamma(\alpha, \rho).$$
Usage
pFTG(x, threshold, scale, shape)
Arguments
x
Sample data.
threshold
Minimum value of the tail.
scale
Scale parameter.
shape
Shape parameter.
Value
Gives the distribution function 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>.