The psubbo returns the Cumulative Distribution Function (CDF) from the
the Subbotin evaluated at \(a\) and return \(z\), such that
\(P(X < a) = z\).
psubbo(x, m = 0, a = 1, b = 2)a vector containing the values for the probabilities.
(numeric) - value in the range \((-\infty, \infty)\) to evaluate the density.
(numeric) - location parameter.
(numeric) - scale parameter. Must be in the range \((0, \infty)\).
(numeric) - shape parameter. Must be in the range \((0, \infty)\).
The Subbotin cumulative distribution function is given by: $$F(x;a,b,m) = 0.5 + 0.5 \text{sign}(x -m)P(x, 1/b)$$ where \(P\) is the normalized incomplete gamma function: $$P(x, 1/b) = 1 - \frac{1}{\Gamma(1/b)} \int_{0}^{x} t^{1/b -1}e^{-t} $$ and \(a\) is a scale parameter, \(b\) controls the tails (lower values represent fatter tails), and \(m\) is a location parameter.