The Beta Transformed Lomax distribution

The Beta Transformed Lomax family

Usage

BTL(mu.link = "log", sigma.link = "log", nu.link = "log")

Arguments

mu.link: defines the mu.link, with "log" link as the default for the mu parameter.
sigma.link: defines the sigma.link, with "log" link as the default for the sigma parameter.
nu.link: defines the nu.link, with "log" link as the default for the nu parameter.

Value

Returns a gamlss.family object which can be used to fit a BTL distribution in the gamlss() function.

Details

The Beta Transformed Lomax distribution with parameters mu, sigma and nu has density given by

\(f(x) = \frac{\log \nu}{\nu-1} \frac{\sigma}{\mu} \left(1+\frac{x}{\mu}\right)^{-(\sigma+1)} \nu^{\left(1+\frac{x}{\mu}\right)^{-\sigma}},\)

for \(\nu \neq 1\), and for \(\nu = 1\):

\(f(x) = \frac{\sigma}{\mu} \left(1+\frac{x}{\mu}\right)^{-(\sigma+1)},\)

for \(x \geq 0\), \(\mu > 0\), \(\sigma > 0\) and \(\nu > 0\).

References

Kottakkunnan, F. A New Generalization of Lomax Distribution: Estimation and Modelling for Medical Data. J Stat Theory Appl 25, 19 (2026). https://doi.org/10.1007/s44199-026-00171-0

Author

Marieth Guillen, mguillen@unal.edu.co

Examples

# Example 1
# Generating some random values with
# known mu and sigma

hist(rnorm(1000))