dGGEO {DiscreteDists} | R Documentation |
The GGEO distribution
Description
These functions define the density, distribution function, quantile
function and random generation for the Generalized Geometric distribution
with parameters \mu
and \sigma
.
Usage
dGGEO(x, mu = 0.5, sigma = 1, log = FALSE)
pGGEO(q, mu = 0.5, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rGGEO(n, mu = 0.5, sigma = 1)
qGGEO(p, mu = 0.5, sigma = 1, lower.tail = TRUE, log.p = FALSE)
Arguments
x , q |
vector of (non-negative integer) quantiles. |
mu |
vector of the mu parameter. |
sigma |
vector of the sigma parameter. |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
n |
number of random values to return. |
p |
vector of probabilities. |
Details
The GGEO distribution with parameters \mu
and \sigma
has a support 0, 1, 2, ... and mass function given by
f(x | \mu, \sigma) = \frac{\sigma \mu^x (1-\mu)}{(1-(1-\sigma) \mu^{x+1})(1-(1-\sigma) \mu^{x})}
with 0 < \mu < 1
and \sigma > 0
. If \sigma=1
, the GGEO distribution
reduces to the geometric distribution with success probability 1-\mu
.
Note: in this implementation we changed the original parameters
\theta
for \mu
and \alpha
for \sigma
,
we did it to implement this distribution within gamlss framework.
Value
dGGEO
gives the density, pGGEO
gives the distribution
function, qGGEO
gives the quantile function, rGGEO
generates random deviates.
Author(s)
Valentina Hurtado Sepulveda, vhurtados@unal.edu.co
References
Gómez-Déniz E (2010). “Another generalization of the geometric distribution.” Test, 19, 399-415.
See Also
GGEO.
Examples
# Example 1
# Plotting the mass function for different parameter values
x_max <- 80
probs1 <- dGGEO(x=0:x_max, mu=0.5, sigma=10)
probs2 <- dGGEO(x=0:x_max, mu=0.7, sigma=30)
probs3 <- dGGEO(x=0:x_max, mu=0.9, sigma=50)
# To plot the first k values
plot(x=0:x_max, y=probs1, type="o", lwd=2, col="dodgerblue", las=1,
ylab="P(X=x)", xlab="X", main="Probability for GGEO",
ylim=c(0, 0.20))
points(x=0:x_max, y=probs2, type="o", lwd=2, col="tomato")
points(x=0:x_max, y=probs3, type="o", lwd=2, col="green4")
legend("topright", col=c("dodgerblue", "tomato", "green4"), lwd=3,
legend=c("mu=0.5, sigma=10",
"mu=0.7, sigma=30",
"mu=0.9, sigma=50"))
# Example 2
# Checking if the cumulative curves converge to 1
x_max <- 10
plot_discrete_cdf(x=0:x_max,
fx=dGGEO(x=0:x_max, mu=0.3, sigma=15),
col="dodgerblue",
main="CDF for GGEO",
lwd= 3)
legend("bottomright", legend="mu=0.3, sigma=15", col="dodgerblue",
lty=1, lwd=2, cex=0.8)
plot_discrete_cdf(x=0:x_max,
fx=dGGEO(x=0:x_max, mu=0.5, sigma=30),
col="tomato",
main="CDF for GGEO",
lwd=3)
legend("bottomright", legend="mu=0.5, sigma=30",
col="tomato", lty=1, lwd=2, cex=0.8)
plot_discrete_cdf(x=0:x_max,
fx=dGGEO(x=0:x_max, mu=0.5, sigma=50),
col="green4",
main="CDF for GGEO",
lwd=3)
legend("bottomright", legend="mu=0.5, sigma=50",
col="green4", lty=1, lwd=2, cex=0.8)
# Example 3
# Comparing the random generator output with
# the theoretical probabilities
x_max <- 15
probs1 <- dGGEO(x=0:x_max, mu=0.5, sigma=5)
names(probs1) <- 0:x_max
x <- rGGEO(n=1000, mu=0.5, sigma=5)
probs2 <- prop.table(table(x))
cn <- union(names(probs1), names(probs2))
height <- rbind(probs1[cn], probs2[cn])
nombres <- cn
mp <- barplot(height, beside=TRUE, names.arg=nombres,
col=c("dodgerblue3", "firebrick3"), las=1,
xlab="X", ylab="Proportion")
legend("topright",
legend=c("Theoretical", "Simulated"),
bty="n", lwd=3,
col=c("dodgerblue3","firebrick3"), lty=1)
# Example 4
# Checking the quantile function
mu <- 0.5
sigma <- 5
p <- seq(from=0, to=1, by=0.01)
qxx <- qGGEO(p=p, mu=mu, sigma=sigma, lower.tail=TRUE, log.p=FALSE)
plot(p, qxx, type="s", lwd=2, col="green3", ylab="quantiles",
main="Quantiles of GGEO(mu=0.5, sigma=0.5)")