Description Usage Arguments Details Value Author(s) References Examples

Density, distribution function, quantile function and random generation for the Marshall-Olkin extended extreme value distribution (MOEEV) distribution with location parameter mu, scale parameter sigma and tilt paramater alpha.

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`x, q` |
vector of quantiles. |

`mu` |
vector of location parameters. |

`sigma` |
vector of scale parameters. |

`alpha` |
vector of tilt parameters. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`p` |
vector of probabilities. |

`n` |
number of observations. If length(n) > 1, the length is taken to be the number required. |

`lower.tail` |
logical; if TRUE (default), probabilities are |

The Marshall-Olkin Extended Extreme Value (MOEEV) distribution has density

*f(x;μ,σ,α) = {α
exp[w-exp(w)]} / {σ x{1-(1-α)exp[-exp(w)]}^2}, x>0*

where *w=[log(x)-μ]/σ* and
*-∞<μ<∞*, *σ>0* and *α>0* are the location, scale and tilt
parameters, respectively. If *α = 1*, we obtain the extreme value distribution.

Consider the parameterisations used by `dexp`

and `dweibull`

.
If *μ = -log(rate)* and *σ = 1*, we obtain the
Marshall-Olkin Extended Exponential (MOEE) distribution. In the case, that
*μ = log(scale)* and *σ = 1/shape*,
we obtain the Marshall-Olkin Extended Weibull (MOEW) distribution. With the above definitions,

if MOEE:
`dmoeev(x, mu = -log(rate), sigma = 1, alpha) = dmoee(x, mu, alpha)`

if MOEW:
`dmoeev(x, mu = log(scale), sigma = 1/shape, alpha)`

The Marshall-Olkin extended extreme value distribution simplifies to the exponential and Weibull distributions with the following parameterisations:

`dmoeev(x, mu, sigma = 1, alpha = 1)` | ` = ` | `dexp(x, rate = 1/exp(mu))` |

`dmoeev(x, mu, sigma, alpha = 1)` | ` = ` | `dweibull(x, shape=1/sigma, scale=exp(mu))` |

`dmoeev`

gives the density, `pmoeev`

gives the distribution function, `qmoeev`

gives the quantile
function, and `rmoeev`

generates random deviates.

Rumenick Pereira da Silva [email protected]

Marshall, A. W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the Weibull and Weibull families. Biometrika,84(3):641-652.

Marshall, A. W., Olkin, I.(2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. Springer, New York.

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Rumenick/flexcure documentation built on July 9, 2018, 2:20 p.m.

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