[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 can be created by calls of the form new("Pareto", shape, Min)
.
More frequently they are created via the generating function
Pareto
.
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
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
signature(.Object = "Pareto")
: initialize method.
signature(object = "Pareto")
: wrapped access method for
slot shape
of slot param
.
signature(x = "Pareto")
: wrapped access method for
slot Min
of slot param
.
signature(x = "Pareto")
: wrapped access method for
slot Min
of slot param
.
signature(object = "Pareto")
: wrapped replace method for
slot shape
of slot param
.
signature(x = "Pareto")
: wrapped replace method for
slot Min
of slot param
.
signature(object = "Pareto", fun = "missing", cond = "missing")
:
exact evaluation using explicit expressions.
signature(signature(x = "Pareto")
:
exact evaluation using explicit expressions.
signature(signature(x = "Pareto")
:
exact evaluation using explicit expressions.
signature(signature(x = "Pareto")
:
exact evaluation using explicit expressions.
signature(signature(x = "Pareto")
:
exact evaluation using explicit expressions.
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
.
signature(object = "Pareto", x = "numeric")
:
checks if x
lies in the support of the respective distribution.
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.
# NOT RUN {
(P1 <- new("Pareto", shape = 1, Min = 2))
plot(P1)
shape(P1)
Min(P1)
shape(P1) <- 4
Min(P1) <- 2
plot(P1)
# }
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