Description Usage Arguments Details Value Author(s) Source References See Also Examples

Density, distribution function, quantile function and random generation
for the KumW distribution with parameters `lambda`

, `phi`

,
`c`

, `k`

and `s`

.

1 2 3 4 5 6 7 8 9 10 11 |

`x, q` |
numeric vector of quantiles. |

`beta` |
scale parameter |

`c` |
shape parameter |

`lambda` |
shape parameter |

`phi` |
shape parameter |

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

`lower.tail` |
logical; if |

`n` |
desired size of the random number sample. |

`cens.prop` |
proportion of censored data to be simulated. If greater than |

The KumW distribution was described by Cordeiro *et al* (2010) and has density

*f(x) = λφcβ^cx^(x-1)e^(-(βx)^c)(1-e^(-(βx)^c))^(λ-1)
(1-(1-e^(-(βx)^c))^λ)^(φ-1)*

with scale parameter *β*, shape parameters *λ*, *φ* and
*c*. The parameters *λ* and *phi*, come from the Kumaraswamy
Generalized family introduced by Cordeiro and Castro (2011).

The KumW is a special case of KumBII introduced by Parna<c3><ad>ba *et al* (2013).

With `phi = 1`

KumW becomes the Exponentiated Weibull distribution.
In addition, when `lambda = 1`

it becomes the Weibull distribution.

When `phi = c = 1`

then the KumW distribution becomes the exponentiated exponential
distribution .

The above are arguably the most important sub-models to KumW. More su-models are decribed
by Cordeiro *et al* (2010) as well as some expasions for the KumW pdf.

`dkumw`

gives the density, `pkumw`

gives the distribution
function, `qkumw`

gives the quantile function, and `rkumw`

generates random values.

The length of the result is determined by `n`

for `rkumw`

, for the other fucntions the
length is the same as the vector passed to the first argument.

Only the first element of the logical arguments are used.

Anderson Neisse <[email protected]>

The source code of all distributions in this package can also be found on the survdistr Github repository.

CORDEIRO, G. M.; ORTEGA, E. M. M; NADARAJAH, S.. The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 2010, 347.8: 1399-1429.

PARANA<c3><8d>BA, P. F.; Ortega, E. M.; Cordeiro, G. M.; Pascoa, M. A. D. The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 2013, 83.11: 2117-2143.

CORDEIRO, G. M.; DE CASTRO, M. A new family of generalized distributions. Journal of statistical computation and simulation, 2011, 81.7: 883-898.

LINK TO OTHER PACKAGE DISTRIBUTIONS

1 2 3 4 5 6 7 8 9 | ```
# Equivalency with the Weibull
all.equal(dkumw(5, beta = 0.5, c = 2, lambda = 1, phi = 1),
dweibull(5, shape = 2, scale = 1/0.5))
# Generating values and comparing with the function
x <- rkumw(10000, beta = 1.5, c = 0.5, lambda = 3, phi = 10)
hist(x, probability = T, breaks = 100)
curve(dkumw(x, beta = 1.5, c = 0.5, lambda = 3, phi = 10),
from = 0, to = 2, add = T)
``` |

aneisse/survdistr documentation built on May 22, 2019, 2:16 p.m.

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