InverseGamma {actuar} | R Documentation |

Density function, distribution function, quantile function, random generation,
raw moments, and limited moments for the Inverse Gamma distribution
with parameters `shape`

and `scale`

.

dinvgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE) pinvgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) qinvgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) rinvgamma(n, shape, rate = 1, scale = 1/rate) minvgamma(order, shape, rate = 1, scale = 1/rate) levinvgamma(limit, shape, rate = 1, scale = 1/rate, order = 1) mgfinvgamma(t, shape, rate =1, scale = 1/rate, log =FALSE)

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

`shape, scale` |
parameters. Must be strictly positive. |

`rate` |
an alternative way to specify the scale. |

`log, log.p` |
logical; if |

`lower.tail` |
logical; if |

`order` |
order of the moment. |

`limit` |
limit of the loss variable. |

`t` |
numeric vector. |

The inverse gamma distribution with parameters `shape`

*= a* and `scale`

*= s* has density:

*
f(x) = u^a exp(-u)/(x Gamma(a)), u = s/x*

for *x > 0*, *a > 0* and *s > 0*.
(Here *Gamma(a)* is the function implemented
by **R**'s `gamma()`

and defined in its help.)

The special case `shape == 1`

is an
Inverse Exponential distribution.

The *k*th raw moment of the random variable *X* is
*E[X^k]*, *k < shape*, and the *k*th
limited moment at some limit *d* is *E[min(X,
d)^k]*, all *k*.

The moment generating function is given by *E[e^{tX}]*.

`dinvgamma`

gives the density,
`pinvgamma`

gives the distribution function,
`qinvgamma`

gives the quantile function,
`rinvgamma`

generates random deviates,
`minvgamma`

gives the *k*th raw moment,
`levinvgamma`

gives the *k*th moment of the limited loss
variable, and
`mgfinvgamma`

gives the moment generating function in `t`

.

Invalid arguments will result in return value `NaN`

, with a warning.

`levinvgamma`

computes the limited expected value using
`gammainc`

from package expint.

Also known as the Vinci distribution. See also Kleiber and Kotz (2003) for alternative names and parametrizations.

The `"distributions"`

package vignette provides the
interrelations between the continuous size distributions in
actuar and the complete formulas underlying the above functions.

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

Kleiber, C. and Kotz, S. (2003), *Statistical Size Distributions
in Economics and Actuarial Sciences*, Wiley.

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012),
*Loss Models, From Data to Decisions, Fourth Edition*, Wiley.

exp(dinvgamma(2, 3, 4, log = TRUE)) p <- (1:10)/10 pinvgamma(qinvgamma(p, 2, 3), 2, 3) minvgamma(-1, 2, 2) ^ 2 levinvgamma(10, 2, 2, order = 1) mgfinvgamma(-1, 3, 2)

[Package *actuar* version 3.1-4 Index]