psubbo: Returns CDF from Subbotin Distribution

In Rsubbotools: Fast Estimation of Subbottin and AEP Distributions (Generalized Error Distribution)

Returns CDF from Subbotin Distribution

Description

The psubbo returns the Cumulative Distribution Function (CDF) from the the Subbotin evaluated at a and return z, such that P(X < a) = z.

Usage

psubbo(x, m = 0, a = 1, b = 2)

Arguments

x	(numeric) - value in the range (-\infty, \infty) to evaluate the density.
m	(numeric) - location parameter.
a	(numeric) - scale parameter. Must be in the range (0, \infty).
b	(numeric) - shape parameter. Must be in the range (0, \infty).

Details

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.

Value

a vector containing the values for the probabilities.

Rsubbotools documentation built on April 16, 2025, 5:10 p.m.