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

Density, distribution function, quantile function and random generation
for the GeoGG distribution with parameters `tau`

, `alpha`

,
`k`

and `pg`

.

1 2 3 4 5 6 7 8 9 |

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

`alpha` |
scale parameter |

`tau` |
shape parameter |

`k` |
shape parameter |

`pg` |
is the probability of success |

`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 GeoGG distribution has density

*f(x) = ((τ(1-p))/(α Γ(k)))(x/α))^(τ k-1)
e^(-(t/α)^τ)(1 - p*(1-γ(k, (t/α)^τ)))^(-2)*

with scale parameter *α*, shape parameters *τ* and *k* and *p*
is the degeneration parameter as described by Ortega *et al* (2011).

If `alpha`

is not specified it assumes the default value of 1.

With `pg = 0`

GeoGG equals the Generalized Gamma with parameterizantion
described on Stacy's (1962).

When `pg = 0`

and `tau = 1`

then it equals a Gama
with `shape = k`

and `scale = alpha`

.

With `pg = 0`

and `k = 1`

it equals a Weibull with
`shape = tau`

and `scale = alpha`

.

Finally, when `pg = 0`

and `tau = k = 1`

it becomes the
Exponential with `rate = 1/alpha`

.

For the cases described above, when `0 < pg < 1`

then the GeoGG will
result in the Geometrical Gamma, Geometrical Weibull and Geometrical Exponential,
respectively, as described by Ortega *et al* (2011).

`dgeogg`

gives the density, `pgeogg`

gives the distribution
function, `qgeogg`

gives the quantile function, and `rgeogg`

generates random values.

The length of the result is determined by `n`

for `rgeogg`

, 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.

STACY, E. W., et al. A generalization of the gamma distribution. The Annals of mathematical statistics, 1962, 33.3: 1187-1192.

ORTEGA, E. M. M.; CORDEIRO, G. M.; PASCOA, M. A. R. The generalized gamma geometric distribution. Journal of Statistical Theory and Applications, 2011, 10.3: 433-454.

LINK TO OTHER PACKAGE DISTRIBUTIONS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
#Equivalency to the Generalized Gamma on it's original parameterization
all.equal(dgeogg(5, alpha = 2, tau = 3, k = 0.5, pg = 0),
dgengamma.orig(5, shape = 3, scale = 2, k = 0.5))
#Equivalency to the Gamma
all.equal(dgeogg(5, alpha = 2, tau = 1, k = 0.5, pg = 0),
dgamma(5, shape = 0.5, scale = 2))
#Equivalency to the Weibull
all.equal(dgeogg(5, alpha = 2, tau = 3, k = 1, pg = 0),
dweibull(5, shape = 3, scale = 2))
#Equivalency to the Exponential
all.equal(dgeogg(5, alpha = 2, tau = 1, k = 1, pg = 0),
dexp(5, rate = 1/2))
# Generating values and comparing with the function
x <- rgeogg(10000, alpha = 2, tau = 3, k = 0.5, pg = 0.35)
hist(x, probability = T, breaks = 100)
curve(dgeogg(x, alpha = 2, tau = 3, k = 0.5, pg = 0.35),
from = 0, to = 4, add = T)
``` |

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

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.