The truncated Pareto distribution
Density, distribution function, quantile function and random generation for the truncated Pareto distribution.
dtpareto(x, shape, scale = 1, endpoint = Inf, log = FALSE) ptpareto(x, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) qtpareto(p, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) rtpareto(n, shape, scale = 1, endpoint = Inf)
x |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
shape |
The shape parameter of the truncated Pareto distribution, a strictly positive number. |
scale |
The scale parameter of the truncated Pareto distribution, a strictly positive number. Its default value is |
endpoint |
Endpoint of the truncated Pareto distribution. The default value is |
log |
Logical indicating if the densities are given as \log(f), default is |
lower.tail |
Logical indicating if the probabilities are of the form P(X≤ x) ( |
log.p |
Logical indicating if the probabilities are given as \log(p), default is |
The Cumulative Distribution Function (CDF) of the truncated Pareto distribution is equal to F_T(x) = F(x) / F(T) for x ≤ T where F is the CDF of an ordinary Pareto distribution and T is the endpoint (truncation point) of the truncated Pareto distribution.
dtpareto gives the density function evaluated in x, ptpareto the CDF evaluated in x and qtpareto the quantile function evaluated in p. The length of the result is equal to the length of x or p.
rtpareto returns a random sample of length n.
Tom Reynkens
# Plot of the PDF x = seq(1,10,0.01) plot(x, dtpareto(x, shape=2, endpoint=10), xlab="x", ylab="PDF", type="l") # Plot of the CDF x = seq(1,10,0.01) plot(x, ptpareto(x, shape=2, endpoint=10), xlab="x", ylab="CDF", type="l")
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