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)

Arguments

x, q

vector of quantiles.

vector of probabilities.

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.

Value

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.

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.

Examples

Run this code

# 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)
# }

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