VGAM (version 1.1-8)

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)

Value

dposnorm gives the density,

pposnorm gives the distribution function,

qposnorm gives the quantile function, and

rposnorm generates random deviates.

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.

Author

T. W. Yee

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

if (FALSE)  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 the CDF",
     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