shape1, shape2 and scale.
dburr(x, shape1, shape2, rate = 1, scale = 1/rate, log = FALSE)
pburr(q, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qburr(p, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rburr(n, shape1, shape2, rate = 1, scale = 1/rate)
mburr(order, shape1, shape2, rate = 1, scale = 1/rate)
levburr(limit, shape1, shape2, rate = 1, scale = 1/rate, order = 1)length(n) > 1, the length is
taken to be the number required.TRUE, probabilities/densities
$p$ are returned as $log(p)$.TRUE (default), probabilities are
$P[X <= x]$,="" otherwise,="" $p[x=""> x]$.dburr gives the density,
pburr gives the distribution function,
qburr gives the quantile function,
rburr generates random deviates,
mburr gives the $k$th raw moment, and
levburr gives the $k$th moment of the limited loss
variable.Invalid arguments will result in return value NaN, with a warning.
shape1 $= a$, shape2 $= b$ and scale
$= s$ has density:
$$f(x) = \frac{\alpha \gamma (x/\theta)^\gamma}{%
x[1 + (x/\theta)^\gamma]^{\alpha + 1}}$$
for $x > 0$, $a > 0$, $b > 0$
and $s > 0$.The Burr is the distribution of the random variable $$\theta \left(\frac{X}{1 - X}\right)^{1/\gamma},$$ where $X$ has a Beta distribution with parameters $1$ and $a$.
The Burr distribution has the following special cases:
shape1
== 1;
shape2 == shape1;
shape2 ==
1.
The $k$th raw moment of the random variable $X$ is $E[X^k]$ and the $k$th limited moment at some limit $d$ is $E[min(X, d)]$.
exp(dburr(1, 2, 3, log = TRUE))
p <- (1:10)/10
pburr(qburr(p, 2, 3, 2), 2, 3, 2)
mburr(2, 2, 3, 1) - mburr(1, 2, 3, 1) ^ 2
levburr(10, 2, 3, 1, order = 2)
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