VGAM (version 1.1-11)

ParetoIV: 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)

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.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as in runif.

location

the location parameter.

scale, shape, inequality

the (positive) scale, inequality and shape parameters.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Author

T. W. Yee and Kai Huang

Details

For the formulas and other details see paretoIV.

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

paretoIV, Pareto.

Examples

if (FALSE) {
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)
}