distrEx (version 2.3.1)

Pareto-class: Pareto distribution

Description

[borrowed from actuar]: The (Single-parameter) Pareto distribution with parameter shape $= \alpha$ has density: $$f(x) = \frac{\alpha \theta^\alpha}{x^{\alpha + 1}}$$ for $x > \theta$, $\alpha > 0$ and $\theta > 0$. Although there appears to be two parameters, only shape is a true parameter. The value of min $= \theta$ must be set in advance.

Objects from the Class

Objects can be created by calls of the form new("Pareto", shape, Min). More frequently they are created via the generating function Pareto.

Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

concept

• Pareto
• extreme value distribution
• absolutely continuous distribution
• S4 distribution class

References

Johnson et al. (1995) Continuous Univariate Distributions. Vol. 2. 2nd ed. New York: Wiley. Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.

See Also

dpareto1, AbscontDistribution-class

Examples

(P1 <- new("Pareto", shape = 1, Min = 2))
plot(P1)
shape(P1)
Min(P1)
shape(P1) <- 4
Min(P1) <- 2
plot(P1)