InverseBurr {actuar} | R Documentation |

Density function, distribution function, quantile function, random
generation, raw moments and limited moments for the Inverse Burr
distribution with parameters `shape1`

, `shape2`

and
`scale`

.

dinvburr(x, shape1, shape2, rate = 1, scale = 1/rate, log = FALSE) pinvburr(q, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) qinvburr(p, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) rinvburr(n, shape1, shape2, rate = 1, scale = 1/rate) minvburr(order, shape1, shape2, rate = 1, scale = 1/rate) levinvburr(limit, shape1, shape2, rate = 1, scale = 1/rate, order = 1)

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

`shape1, shape2, 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. |

The inverse Burr distribution with parameters `shape1`

*= a*, `shape2`

*= b* and `scale`

*= s*, has density:

*
f(x) = a b (x/s)^(ba)/(x [1 + (x/s)^b]^(a + 1))*

for *x > 0*, *a > 0*, *b > 0* and
*s > 0*.

The inverse Burr is the distribution of the random variable

*
s (X/(1 - X))^(1/b),*

where *X* has a beta distribution with parameters *a*
and *1*.

The inverse Burr distribution has the following special cases:

A Loglogistic distribution when

`shape1 == 1`

;An Inverse Pareto distribution when

`shape2 == 1`

;An Inverse Paralogistic distribution when

`shape1 == shape2`

.

The *k*th raw moment of the random variable *X* is
*E[X^k]*, *-shape1 * shape2
< k < shape2*.

The *k*th limited moment at some limit *d* is *E[min(X, d)^k]*, *k > -shape1 * shape2*
and *1 - k/shape2* not a negative integer.

`dinvburr`

gives the density,
`invburr`

gives the distribution function,
`qinvburr`

gives the quantile function,
`rinvburr`

generates random deviates,
`minvburr`

gives the *k*th raw moment, and
`levinvburr`

gives the *k*th moment of the limited loss
variable.

Invalid arguments will result in return value `NaN`

, with a warning.

`levinvburr`

computes the limited expected value using
`betaint`

.

Also known as the Dagum 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(dinvburr(2, 2, 3, 1, log = TRUE)) p <- (1:10)/10 pinvburr(qinvburr(p, 2, 3, 1), 2, 3, 1) ## variance minvburr(2, 2, 3, 1) - minvburr(1, 2, 3, 1) ^ 2 ## case with 1 - order/shape2 > 0 levinvburr(10, 2, 3, 1, order = 2) ## case with 1 - order/shape2 < 0 levinvburr(10, 2, 1.5, 1, order = 2)

[Package *actuar* version 3.1-4 Index]