ParetoIV {VGAM} | R Documentation |
The Pareto(IV/III/II) Distributions
Description
Density, distribution function, quantile function and random generation for the Pareto(IV/III/II) distributions.
Usage
dparetoIV(x, location = 0, scale = 1, inequality = 1, shape = 1,
log = FALSE)
pparetoIV(q, location = 0, scale = 1, inequality = 1, shape = 1,
lower.tail = TRUE, log.p = FALSE)
qparetoIV(p, location = 0, scale = 1, inequality = 1, shape = 1,
lower.tail = TRUE, log.p = FALSE)
rparetoIV(n, location = 0, scale = 1, inequality = 1, shape = 1)
dparetoIII(x, location = 0, scale = 1, inequality = 1, log = FALSE)
pparetoIII(q, location = 0, scale = 1, inequality = 1,
lower.tail = TRUE, log.p = FALSE)
qparetoIII(p, location = 0, scale = 1, inequality = 1,
lower.tail = TRUE, log.p = FALSE)
rparetoIII(n, location = 0, scale = 1, inequality = 1)
dparetoII(x, location = 0, scale = 1, shape = 1, log = FALSE)
pparetoII(q, location = 0, scale = 1, shape = 1,
lower.tail = TRUE, log.p = FALSE)
qparetoII(p, location = 0, scale = 1, shape = 1,
lower.tail = TRUE, log.p = FALSE)
rparetoII(n, location = 0, scale = 1, shape = 1)
dparetoI(x, scale = 1, shape = 1, log = FALSE)
pparetoI(q, scale = 1, shape = 1,
lower.tail = TRUE, log.p = FALSE)
qparetoI(p, scale = 1, shape = 1,
lower.tail = TRUE, log.p = FALSE)
rparetoI(n, scale = 1, shape = 1)
Arguments
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as in |
location |
the location parameter. |
scale , shape , inequality |
the (positive) scale, inequality and shape parameters. |
log |
Logical.
If |
lower.tail , log.p |
Details
For the formulas and other details
see paretoIV
.
Value
Functions beginning with the
letters d
give the density,
p
give the distribution function,
q
give the quantile function, and
r
generates random deviates.
Note
The functions [dpqr]paretoI
are the same as
[dpqr]pareto
except for a slight change in notation:
s=k
and b=\alpha
; see Pareto
.
Author(s)
T. W. Yee and Kai Huang
References
Brazauskas, V. (2003). Information matrix for Pareto(IV), Burr, and related distributions. Comm. Statist. Theory and Methods 32, 315–325.
Arnold, B. C. (1983). Pareto Distributions. Fairland, Maryland: International Cooperative Publishing House.
See Also
Examples
## Not run:
x <- seq(-0.2, 4, by = 0.01)
loc <- 0; Scale <- 1; ineq <- 1; shape <- 1.0
plot(x, dparetoIV(x, loc, Scale, ineq, shape), type = "l",
main = "Blue is density, orange is the CDF", col = "blue",
sub = "Purple are 5,10,...,95 percentiles", ylim = 0:1,
las = 1, ylab = "")
abline(h = 0, col = "blue", lty = 2)
Q <- qparetoIV(seq(0.05, 0.95,by = 0.05), loc, Scale, ineq, shape)
lines(Q, dparetoIV(Q, loc, Scale, ineq, shape), col = "purple",
lty = 3, type = "h")
lines(x, pparetoIV(x, loc, Scale, ineq, shape), col = "orange")
abline(h = 0, lty = 2)
## End(Not run)