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 α from the Generalized Gama (Stacy, 1962), α > 0. |
tau |
shape parameter τ from the Generalized Gama (Stacy, 1962), τ > 0. |
k |
shape parameter k from the Generalized Gama (Stacy, 1962), k > 0. |
pg |
is the probability of success p from the Geometric, 0 < p < 1. |
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 <a.neisse@gmail.com>
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)
|
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