Exp-class {distr}

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(s)

Thomas Stabla [e-mail],
Florian Camphausen [e-mail],
Peter Ruckdeschel [e-mail],
Matthias Kohl [e-mail]

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)