Pareto-class

0th

Percentile

Pareto distribution

[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.

Keywords
distribution
Note

This class is based on the code provided by the package actuar by Vincent Goulet and Mathieu Pigeon.

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.

Slots

img

Object of class "Reals".

param

Object of class "ParetoParameter".

r

rpareto1

d

dpareto1

p

ppareto1

q

qpareto1

gaps

(numeric) matrix or NULL

.withArith

logical: used internally to issue warnings as to interpretation of arithmetics

.withSim

logical: used internally to issue warnings as to accuracy

.logExact

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

.lowerExact

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

Extends

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

Methods

initialize

signature(.Object = "Pareto"): initialize method.

shape

signature(object = "Pareto"): wrapped access method for slot shape of slot param.

Min

signature(x = "Pareto"): wrapped access method for slot Min of slot param.

scale

signature(x = "Pareto"): wrapped access method for slot Min of slot param.

shape<-

signature(object = "Pareto"): wrapped replace method for slot shape of slot param.

Min<-

signature(x = "Pareto"): wrapped replace method for slot Min of slot param.

E

signature(object = "Pareto", fun = "missing", cond = "missing"): exact evaluation using explicit expressions.

var

signature(signature(x = "Pareto"): exact evaluation using explicit expressions.

median

signature(signature(x = "Pareto"): exact evaluation using explicit expressions.

IQR

signature(signature(x = "Pareto"): exact evaluation using explicit expressions.

skewness

signature(signature(x = "Pareto"): exact evaluation using explicit expressions.

kurtosis

signature(signature(x = "Pareto"): exact evaluation using explicit expressions.

*

signature(e1 = "Pareto", e2 = "numeric"): exact method for this transformation --- stays within this class if e2>0.

liesInSupport

signature(object = "Pareto", x = "numeric"): checks if x lies in the support of the respective distribution.

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

Aliases
  • Pareto-class
  • initialize,Pareto-method
  • shape,Pareto-method
  • shape<-,Pareto-method
  • Min,Pareto-method
  • Min<-,Pareto-method
  • scale,Pareto-method
  • *,Pareto,numeric-method
  • liesInSupport,Pareto,numeric-method
Examples
# NOT RUN {
(P1 <- new("Pareto", shape = 1, Min = 2))
plot(P1)
shape(P1)
Min(P1)
shape(P1) <- 4
Min(P1) <- 2
plot(P1)
# }
Documentation reproduced from package RobExtremes, version 1.2.0, License: LGPL-3

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