Pareto-class | R Documentation |
[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.
This class is based on the code provided by the package actuar by Vincent Goulet and Mathieu Pigeon.
Nataliya Horbenko nhorbenko@gmail.com
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.
dpareto1
, AbscontDistribution-class
(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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