DiscreteDists (version 1.1.1)

dDsPA: The DsPA distribution

Description

These functions define the density, distribution function, quantile function and random generation for the discrete power-Ailamujia distribution with parameters \(\mu\) and \(\sigma\).

Usage

dDsPA(x, mu, sigma, log = FALSE)
pDsPA(q, mu, sigma, lower.tail = TRUE, log.p = FALSE)
qDsPA(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rDsPA(n, mu, sigma)

Value

dDsPA gives the density, pDsPA gives the distribution function, qDsPA gives the quantile function.

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 \(P[X <= x]\), otherwise, \(P[X > x]\).

p

vector of probabilities.

n

number of random values to return.

Author

Maria Camila Mena Romana,

Details

The DsPA distribution with parameters \(\mu\) and \(\sigma\) has a support 0, 1, 2, ...

Note:in this implementation we changed the original parameters \(\beta\) and \(\lambda\) for \(\mu\) and \(\sigma\) respectively, we did it to implement this distribution within gamlss framework.

References

Alghamdi, A. S., Ahsan-ul-Haq, M., Babar, A., Aljohani, H. M., Afify, A. Z., & Cell, Q. E. (2022). The discrete power-Ailamujia distribution: properties, inference, and applications. AIMS Math, 7(5), 8344-8360.

See Also

DsPA.

Examples

# Example 1
# Plotting the mass function for different parameter values

x_max <- 30
probs1 <- dDsPA(x=0:x_max, mu=1.2, sigma=0.5)
probs2 <- dDsPA(x=0:x_max, mu=1.2, sigma=0.7)
probs3 <- dDsPA(x=0:x_max, mu=1.2, sigma=0.9)

# 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 DsPA",
     ylim=c(0, 0.40))
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=1.2, sigma=0.5",
                "mu=1.2, sigma=0.7",
                "mu=1.2, sigma=0.9"))

# Example 2
# Checking if the cumulative curves converge to 1

x_max <- 15
cumulative_probs1 <- pDsPA(q=0:x_max, mu=1.2, sigma=0.5)
cumulative_probs2 <- pDsPA(q=0:x_max, mu=1.2, sigma=0.7)
cumulative_probs3 <- pDsPA(q=0:x_max, mu=1.2, sigma=0.9)

plot(x=0:x_max, y=cumulative_probs1, col="dodgerblue",
     type="o", las=1, ylim=c(0, 1),
     main="Cumulative probability for DsPA",
     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("mu=1.2, sigma=0.5",
                "mu=1.2, sigma=0.7",
                "mu=1.2, sigma=0.9"))

# Example 3
# Comparing the random generator output with
# the theoretical probabilities

x_max <- 50
probs1 <- dDsPA(x=0:x_max, mu=1.2, sigma=0.9)
names(probs1) <- 0:x_max

x <- rDsPA(n=1000, mu=1.2, sigma=0.9)
probs2 <- prop.table(table(x))

cn <- union(names(probs1), names(probs2))
height <- rbind(probs1[cn], probs2[cn])
mp <- barplot(height, beside=TRUE, names.arg=cn,
              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 <- 1.2
sigma <- 0.9
p <- seq(from=0, to=1, by=0.01)
qxx <- qDsPA(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 DsPA(mu=1.2, sigma=0.9)")