The Pareto Distribution
Density, distribution function, quantile function and random generation for the Pareto distribution with scale and shape parameters.
dpareto(x, scale = 1, shape = 1, log = FALSE) ppareto(q, scale = 1, shape = 1, lower.tail = TRUE, log.p = FALSE) qpareto(p, scale = 1, shape = 1, lower.tail = TRUE, log.p = FALSE) rpareto(n, scale = 1, shape = 1)
x, q |
vector of quantiles. |
scale |
scale parameter. |
shape |
shape parameter. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p), default: FALSE. |
lower.tail |
logical; if TRUE, probabilities are P[X ≤ x] otherwise, P[X > x], default: TRUE. |
p |
vector of probabilities. |
n |
number of observations. |
The Pareto distribution function with scale parameter s and shape parameter α has density given by
f(x)=α s^α/x^(α+1)
for x≥ s. The cumulative distribution function is
F(x)=1-(s/x)^α
for x≥ s. See https://en.wikipedia.org/wiki/Pareto_distribution for more details.
dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and
rpareto generates random deviates.
Invalid arguments will result in return value NaN, with a warning.
dpareto(seq(1, 5), 1, 1) qpareto(ppareto(seq(1, 5), 1, 1), 1 ,1) rpareto(5, 1, 1)
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