DExp-class | R Documentation |
The double exponential or Laplace distribution with rate \lambda
has density
f(x) = \frac{1}{2}\lambda {e}^{- \lambda |x|}
C.f. Exp-class
, rexp
Objects can be created by calls of the form DExp(rate)
.
This object is a double exponential (or Laplace) distribution.
img
Object of class "Reals"
:
The space of the image of this distribution has got dimension 1
and the name "Real Space".
param
Object of class "ExpParameter"
:
the parameter of this distribution (rate), declared at its instantiation
r
Object of class "function"
:
generates random numbers (calls function rexp)
d
Object of class "function"
:
density function (calls function dexp)
p
Object of class "function"
:
cumulative function (calls function pexp)
q
Object of class "function"
:
inverse of the cumulative function (calls function qexp)
.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
Symmetry
object of class "DistributionSymmetry"
;
used internally to avoid unnecessary calculations.
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
signature(.Object = "DExp")
:
initialize method
signature(object = "DExp")
:
returns the slot rate of the parameter of the distribution
signature(object = "DExp")
:
modifies the slot rate of the parameter of the distribution
signature(e1 = "DExp", e2 = "numeric")
:
For the Laplace distribution we use its closedness under scaling transformations.
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
Exp-class
ExpParameter-class
AbscontDistribution-class
Reals-class
rexp
D <- DExp(rate = 1) # D is a Laplace distribution with rate = 1.
r(D)(1) # one random number generated from this distribution, e.g. 0.4190765
d(D)(1) # Density of this distribution is 0.1839397 for x = 1.
p(D)(1) # Probability that x < 1 is 0.8160603.
q(D)(.1) # Probability that x < -1.609438 is 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
rate(D) # rate of this distribution is 1.
rate(D) <- 2 # rate of this distribution is now 2.
3*D ### still a DExp -distribution
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