The truncated Burr distribution
Density, distribution function, quantile function and random generation for the truncated Burr distribution (type XII).
dtburr(x, alpha, rho, eta = 1, endpoint = Inf, log = FALSE) ptburr(x, alpha, rho, eta = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) qtburr(p, alpha, rho, eta = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) rtburr(n, alpha, rho, eta = 1, endpoint = Inf)
x |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
alpha |
The α parameter of the truncated Burr distribution, a strictly positive number. |
rho |
The ρ parameter of the truncated Burr distribution, a strictly negative number. |
eta |
The η parameter of the truncated Burr distribution, a strictly positive number.
The default value is |
endpoint |
Endpoint of the truncated Burr 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 Burr distribution is equal to F_T(x) = F(x) / F(T) for x ≤ T where F is the CDF of the ordinary Burr distribution and T is the endpoint (truncation point) of the truncated Burr distribution.
dtburr gives the density function evaluated in x, ptburr the CDF evaluated in x and qtburr the quantile function evaluated in p. The length of the result is equal to the length of x or p.
rtburr returns a random sample of length n.
Tom Reynkens.
# Plot of the PDF x <- seq(0, 10, 0.01) plot(x, dtburr(x, alpha=2, rho=-1, endpoint=9), xlab="x", ylab="PDF", type="l") # Plot of the CDF x <- seq(0, 10, 0.01) plot(x, ptburr(x, alpha=2, rho=-1, endpoint=9), xlab="x", ylab="CDF", type="l")
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