The psep
returns the Cumulative Distribution Function at point x for
the Skewed Exponential Power distribution with parameters \(a\), \(b\).
psep(x, m = 0, a = 2, b = 1, lambda = 0)
a vector containing the values for the probabilities.
vector with values to evaluate CDF.
the location parameter.
the scale parameter.
the shape parameter
the skewness parameter.
The SEP is a exponential power distribution controlled by four parameters, with formula: $$ f(x; m, b, a, \lambda) = 2 \Phi(w) e^{-|z|^b/b}/(c)$$ where: $$z = (x-m)/a$$ $$w = sign(z) |z|^{(b/2)} \lambda \sqrt{2/b}$$ $$c = 2 ab^{(1/b)-1} \Gamma(1/b)$$ with \(\Phi\) the cumulative normal distribution with mean zero and variance one. The CDF is calculated through numerical integration using the 'GSL' suite.