VGAM (version 1.0-1)

Posnorm: The Positive-Normal Distribution

Description

Density, distribution function, quantile function and random generation for the univariate positive-normal distribution.

Usage

dposnorm(x, mean = 0, sd = 1, log = FALSE)
pposnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
qposnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
rposnorm(n, mean = 0, sd = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1 then the length is taken to be the number required.

mean, sd, log, lower.tail, log.p

see rnorm.

Value

• dposnorm gives the density, pposnorm gives the distribution function, qposnorm gives the quantile function, and rposnorm generates random deviates.

Details

See posnormal, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

See Also

posnormal.

Examples

m <-  0.8; x <- seq(-1, 4, len = 501)
plot(x, dposnorm(x, m = m), type = "l", las = 1, ylim = 0:1,
     ylab = paste("posnorm(m = ", m, ", sd = 1)"), col = "blue",
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles")
abline(h = 0, col = "grey")
lines(x, pposnorm(x, m = m), col = "orange", type = "l")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qposnorm(probs, m = m)
lines(Q, dposnorm(Q, m = m), col = "purple", lty = 3, type = "h")
lines(Q, pposnorm(Q, m = m), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pposnorm(Q, m = m) - probs))  # Should be 0