| Benini {VGAM} | R Documentation |
Density, distribution function, quantile function and random
generation for the Benini distribution with parameter
shape.
dbenini(x, shape, y0) pbenini(q, shape, y0) qbenini(p, shape, y0) rbenini(n, shape, y0)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. Must be a positive integer of length 1. |
shape |
the shape parameter b. |
y0 |
the scale parameter y0. |
See benini, the VGAM family function
for estimating the parameter b by maximum likelihood estimation,
for the formula of the probability density function and other details.
dbenini gives the density,
pbenini gives the distribution function,
qbenini gives the quantile function, and
rbenini generates random deviates.
T. W. Yee
Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ: Wiley-Interscience.
## Not run:
y0 = 1
shape = exp(1)
x = seq(-0.0, 4, len=101)
plot(x, dbenini(x, y0=y0,shape=shape), type="l", col="blue", las=1,
main="Blue is density, red is cumulative distribution function",
sub="Purple lines are the 10,20,...,90 percentiles", ylim=0:1,
ylab="")
abline(h=0, col="blue", lty=2)
lines(x, pbenini(x, y0=y0,shape=shape), col="red")
probs = seq(0.1, 0.9, by=0.1)
Q = qbenini(probs, y0=y0,shape=shape)
lines(Q, dbenini(Q, y0=y0,shape=shape), col="purple", lty=3, type="h")
pbenini(Q, y0=y0,shape=shape) - probs # Should be all zero
## End(Not run)