Pareto distribution
Density, distribution function, quantile function and random generation for the Pareto distribution where a, loc and scale are respectively the shape, the location and the scale parameters.
ppareto(q, a = 1, loc = 0, scale = 1) dpareto(x, a = 1, loc = 0, scale = 1) qpareto(p, a = 1, loc = 0, scale = 1) rpareto(n, a = 1, loc = 0, scale = 1)
q |
a vector of quantiles. |
a |
a vector of shape parameter of the Pareto distribution. |
loc |
a vector of location parameter of the Pareto distribution. |
scale |
a vector of scale parameter of the Pareto distribution. |
x |
a vector of quantiles. |
p |
a vector of probabilities. |
n |
a number of observations. If length(n) > 1, the length is taken to be the number required. |
If shape, loc or scale parameters are not specified, the respective default values are 1, 0 and 1.
The cumulative Pareto distribution is
F(x) = 1- ((x-loc)/scale) ^ {-a}, x > loc, a > 0, scale > 0
where a is the shape of the distribution.
The density of the Pareto distribution is
f(x) = (((x-loc)/scale)^( - a - 1) * a/scale) * (x-loc >= scale), x > loc, a > 0, scale > 0
dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and rpareto generates random deviates.
The length of the result is determined by n for rpareto, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
par(mfrow = c(3,1))
plot(function(x) dpareto(x), 1, 5,ylab="density",
main = " Pareto density ")
plot(function(x) ppareto(x), 1, 5,ylab="distribution function",
main = " Pareto Cumulative ")
plot(function(x) qpareto(x), 0, 1,ylab="quantile",
main = " Pareto Quantile ")
#generate a sample of pareto distribution of size n
n <- 100
x <- rpareto(n)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.