The Pareto(IV/III/II) Distributions
Density, distribution function, quantile function and random generation for the Pareto(IV/III/II) distributions.
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)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 |
For the formulas and other details
see paretoIV.
Functions beginning with the letter d give the density,
functions beginning with the letter p give the distribution function,
functions beginning with the letter q give the quantile function, and
functions beginning with the letter r generates random deviates.
The functions [dpqr]paretoI are the same as [dpqr]pareto
except for a slight change in notation: s=k and
b=alpha; see Pareto.
T. W. Yee and Kai Huang
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.
## 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", col = "blue",
main = "Blue is density, orange is cumulative distribution function",
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.