Description Objects from the Class Slots Extends Methods Author(s) See Also Examples

The Gammad distribution with parameters `shape`

*= a*,
by default `= 1`

, and `scale`

*= s*, by default `= 1`

, has
density

*d(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)*

for *x > 0*, *a > 0* and *s > 0*.
The mean and variance are
*E(X) = a*s* and
*Var(X) = a*s^2*. C.f. `rgamma`

Objects can be created by calls of the form `Gammad(scale, shape)`

.
This object is a gamma 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

`"GammaParameter"`

: the parameter of this distribution (scale and shape), declared at its instantiation`r`

Object of class

`"function"`

: generates random numbers (calls function rgamma)`d`

Object of class

`"function"`

: density function (calls function dgamma)`p`

Object of class

`"function"`

: cumulative function (calls function pgamma)`q`

Object of class

`"function"`

: inverse of the cumulative function (calls function qgamma)`.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 `"ExpOrGammaOrChisq"`

, directly.

Class `"AbscontDistribution"`

, by class `"ExpOrGammaOrChisq"`

.

Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.

Class `"Distribution"`

, by class `"UnivariateDistribution"`

.

- initialize
`signature(.Object = "Gammad")`

: initialize method- scale
`signature(object = "Gammad")`

: returns the slot`scale`

of the parameter of the distribution- scale<-
`signature(object = "Gammad")`

: modifies the slot`scale`

of the parameter of the distribution- shape
`signature(object = "Gammad")`

: returns the slot`shape`

of the parameter of the distribution- shape<-
`signature(object = "Gammad")`

: modifies the slot`shape`

of the parameter of the distribution- +
`signature(e1 = "Gammad", e2 = "Gammad")`

: For the Gamma distribution we use its closedness under convolutions.- *
`signature(e1 = "Gammad", e2 = "numeric")`

: For the Gamma distribution we use its closedness under positive scaling transformations.

Thomas Stabla [email protected],

Florian Camphausen [email protected],

Peter Ruckdeschel [email protected],

Matthias Kohl [email protected]

`GammaParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rgamma`

1 2 3 4 5 6 7 8 | ```
G <- Gammad(scale=1,shape=1) # G is a gamma distribution with scale=1 and shape=1.
r(G)(1) # one random number generated from this distribution, e.g. 0.1304441
d(G)(1) # Density of this distribution is 0.3678794 for x=1.
p(G)(1) # Probability that x<1 is 0.6321206.
q(G)(.1) # Probability that x<0.1053605 is 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
scale(G) # scale of this distribution is 1.
scale(G) <- 2 # scale of this distribution is now 2.
``` |

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