R: Class "Exp"

Exp-class {distr} | R Documentation

## Class "Exp"

### Description

The exponential distribution with rate λ has density

f(x) = lambda e^(- lambda x)

for x ≥ 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 statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de

### 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)

[Package distr version 2.8.0 Index]