dPOISXL {DiscreteDists} | R Documentation |
The Discrete Poisson XLindley
Description
These functions define the density, distribution function, quantile
function and random generation for the Discrete Poisson XLindley distribution
with parameter \mu
.
Usage
dPOISXL(x, mu = 0.3, log = FALSE)
pPOISXL(q, mu = 0.3, lower.tail = TRUE, log.p = FALSE)
qPOISXL(p, mu = 0.3, lower.tail = TRUE, log.p = FALSE)
rPOISXL(n, mu = 0.3)
Arguments
x , q |
vector of (non-negative integer) quantiles. |
mu |
vector of the mu parameter. |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of random values to return |
Details
The Discrete Poisson XLindley distribution with parameters \mu
has a support
0, 1, 2, ... and mass function given by
f(x | \mu) = \frac{\mu^2(x+\mu^2+3(1+\mu))}{(1+\mu)^{4+x}}
; with \mu>0
.
Note: in this implementation we changed the original parameters \alpha
for \mu
,
we did it to implement this distribution within gamlss framework.
Value
dPOISXL
gives the density, pPOISXL
gives the distribution
function, qPOISXL
gives the quantile function, rPOISXL
generates random deviates.
Author(s)
Mariana Blandon Mejia, mblandonm@unal.edu.co
References
Ahsan-ul-Haq M, Al-Bossly A, El-Morshedy M, Eliwa MS, others (2022). “Poisson XLindley distribution for count data: statistical and reliability properties with estimation techniques and inference.” Computational Intelligence and Neuroscience, 2022.
See Also
Examples
# Example 1
# Plotting the mass function for different parameter values
x_max <- 20
probs1 <- dPOISXL(x=0:x_max, mu=0.2)
probs2 <- dPOISXL(x=0:x_max, mu=0.5)
probs3 <- dPOISXL(x=0:x_max, mu=1.0)
# 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 Poisson XLindley",
ylim=c(0, 0.50))
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=0.2", "mu=0.5", "mu=1.0"))
# Example 2
# Checking if the cumulative curves converge to 1
x_max <- 20
plot_discrete_cdf(x=0:x_max,
fx=dPOISXL(x=0:x_max, mu=0.2), col="dodgerblue",
main="CDF for Poisson XLindley with mu=0.2")
plot_discrete_cdf(x=0:x_max,
fx=dPOISXL(x=0:x_max, mu=0.5), col="tomato",
main="CDF for Poisson XLindley with mu=0.5")
plot_discrete_cdf(x=0:x_max,
fx=dPOISXL(x=0:x_max, mu=1.0), col="green4",
main="CDF for Poisson XLindley with mu=1.0")
# Example 3
# Comparing the random generator output with
# the theoretical probabilities
x_max <- 15
probs1 <- dPOISXL(x=0:x_max, mu=0.3)
names(probs1) <- 0:x_max
x <- rPOISXL(n=3000, mu=0.3)
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 <- 0.3
p <- seq(from=0, to=1, by = 0.01)
qxx <- qPOISXL(p, mu, lower.tail = TRUE, log.p = FALSE)
plot(p, qxx, type="s", lwd=2, col="green3", ylab="quantiles",
main="Quantiles for Poisson XLindley mu=0.3")