tBurr function

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)

Arguments

• x: Vector of quantiles.
• p: Vector of probabilities.
• n: Number of observations.
• alpha: The $\alpha$ parameter of the truncated Burr distribution, a strictly positive number.
• rho: The $\rho$ parameter of the truncated Burr distribution, a strictly negative number.
• eta: The $\eta$ parameter of the truncated Burr distribution, a strictly positive number. The default value is 1.
• endpoint: Endpoint of the truncated Burr distribution. The default value is Inf for which the truncated Burr distribution corresponds to the ordinary Burr distribution.
• log: Logical indicating if the densities are given as $\log(f)$, default is FALSE.
• lower.tail: Logical indicating if the probabilities are of the form $P(X\le x)$ (TRUE) or $P(X>x)$ (FALSE). Default is TRUE.
• log.p: Logical indicating if the probabilities are given as $\log(p)$, default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the truncated Burr distribution is equal to $F_T(x) = F(x) / F(T)$ for $x \le T$ where $F$ is the CDF of the ordinary Burr distribution and $T$ is the endpoint (truncation point) of the truncated Burr distribution.

Returns

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 $n$.

Author(s)

Tom Reynkens.

See Also

Burr, Distributions

Examples

# 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")