dHYPERPO2 {DiscreteDists} | R Documentation |
The hyper-Poisson distribution (with mu as mean)
Description
These functions define the density, distribution function, quantile
function and random generation for the hyper-Poisson in
the second parameterization with parameters \mu
(as mean) and
\sigma
as the dispersion parameter.
Usage
dHYPERPO2(x, mu = 1, sigma = 1, log = FALSE)
pHYPERPO2(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rHYPERPO2(n, mu = 1, sigma = 1)
qHYPERPO2(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
Arguments
x , q |
vector of (non-negative integer) quantiles. |
mu |
vector of positive values of this parameter. |
sigma |
vector of positive values of this 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 hyper-Poisson distribution with parameters \mu
and \sigma
has a support 0, 1, 2, ...
Note: in this implementation the parameter \mu
is the mean
of the distribution and \sigma
corresponds to
the dispersion parameter. If you fit a model with this parameterization,
the time will increase because an internal procedure to convert \mu
to \lambda
parameter.
Value
dHYPERPO2
gives the density, pHYPERPO2
gives the distribution
function, qHYPERPO2
gives the quantile function, rHYPERPO2
generates random deviates.
Author(s)
Freddy Hernandez, fhernanb@unal.edu.co
References
Sáez-Castillo AJ, Conde-Sánchez A (2013). “A hyper-Poisson regression model for overdispersed and underdispersed count data.” Computational Statistics & Data Analysis, 61, 148–157.
See Also
Examples
# Example 1
# Plotting the mass function for different parameter values
x_max <- 30
probs1 <- dHYPERPO2(x=0:x_max, sigma=0.01, mu=3)
probs2 <- dHYPERPO2(x=0:x_max, sigma=0.50, mu=5)
probs3 <- dHYPERPO2(x=0:x_max, sigma=1.00, mu=7)
# 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 hyper-Poisson",
ylim=c(0, 0.30))
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("sigma=0.01, mu=3",
"sigma=0.50, mu=5",
"sigma=1.00, mu=7"))
# Example 2
# Checking if the cumulative curves converge to 1
x_max <- 15
cumulative_probs1 <- pHYPERPO2(q=0:x_max, mu=1, sigma=1.5)
cumulative_probs2 <- pHYPERPO2(q=0:x_max, mu=3, sigma=1.5)
cumulative_probs3 <- pHYPERPO2(q=0:x_max, mu=5, sigma=1.5)
plot(x=0:x_max, y=cumulative_probs1, col="dodgerblue",
type="o", las=1, ylim=c(0, 1),
main="Cumulative probability for hyper-Poisson",
xlab="X", ylab="Probability")
points(x=0:x_max, y=cumulative_probs2, type="o", col="tomato")
points(x=0:x_max, y=cumulative_probs3, type="o", col="green4")
legend("bottomright", col=c("dodgerblue", "tomato", "green4"), lwd=3,
legend=c("sigma=1.5, mu=1",
"sigma=1.5, mu=3",
"sigma=1.5, mu=5"))
# Example 3
# Comparing the random generator output with
# the theoretical probabilities
x_max <- 15
probs1 <- dHYPERPO2(x=0:x_max, mu=3, sigma=1.1)
names(probs1) <- 0:x_max
x <- rHYPERPO2(n=1000, mu=3, sigma=1.1)
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 <- 3
sigma <-3
p <- seq(from=0, to=1, by=0.01)
qxx <- qHYPERPO2(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 HP2(mu = sigma = 3)")