distr (version 2.8.0)

Exp-class: Class "Exp"

Description

The exponential distribution with rate \(\lambda\) has density $$ f(x) = \lambda {e}^{- \lambda x}$$ for \(x \ge 0\).

C.f. rexp

Objects from the Class

Objects can be created by calls of the form Exp(rate). This object is an exponential distribution.

Slots

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.

Extends

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

Is-Relations

By means of setIs, R ``knows'' that a distribution object obj of class "Exp" also is a Gamma distribution with parameters shape = 1, scale = 1/rate(obj) and a Weibull distribution with parameters shape = 1, scale = 1/rate(obj)

Methods

initialize

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

rate

signature(object = "Exp"): returns the slot rate of the parameter of the distribution

rate<-

signature(object = "Exp"): modifies the slot rate of the parameter of the distribution

*

signature(e1 = "Exp", e2 = "numeric"): For the exponential distribution we use its closedness under positive scaling transformations.

Author

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

See Also

ExpParameter-class AbscontDistribution-class Reals-class rexp

Examples

E <- Exp(rate = 1) # E is a exp distribution with rate = 1.
r(E)(1) # one random number generated from this distribution, e.g. 0.4190765
d(E)(1) # Density of this distribution is 0.3678794 for x = 1.
p(E)(1) # Probability that x < 1 is 0.6321206.
q(E)(.1) # Probability that x < 0.1053605 is 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
rate(E) # rate of this distribution is 1.
rate(E) <- 2 # rate of this distribution is now 2.
is(E, "Gammad") # yes
as(E,"Gammad")
is(E, "Weibull") 
E+E+E ###  a Gammad -distribution
2*E+Gammad(scale=1)

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