The Reverse Weibull Distribution
Density function, distribution function, quantile function and random generation for the reverse (or negative) Weibull distribution with location, scale and shape parameters.
dRevWeibull(x, loc=0, scale=1, shape=1, log = FALSE) pRevWeibull(q, loc=0, scale=1, shape=1, lower.tail = TRUE) qRevWeibull(p, loc=0, scale=1, shape=1, lower.tail = TRUE) rRevWeibull(n, loc=0, scale=1, shape=1) dNegWeibull(x, loc=0, scale=1, shape=1, log = FALSE) pNegWeibull(q, loc=0, scale=1, shape=1, lower.tail = TRUE) qNegWeibull(p, loc=0, scale=1, shape=1, lower.tail = TRUE) rNegWeibull(n, loc=0, scale=1, shape=1)
x, q |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
loc, scale, shape |
Location, scale and shape parameters (can be given as vectors). |
log |
Logical; if |
lower.tail |
Logical; if |
The reverse (or negative) Weibull distribution function with parameters loc = a, scale = b and shape = s is
G(x) = exp{-[-(z-a)/b]^s}
for z < a and one otherwise, where b > 0 and s > 0.
dRevWeibull and dNegWeibull give the density function,
pRevWeibull and pNegWeibull give the distribution function,
qRevWeibull and qNegWeibull give the quantile function,
rRevWeibull and rNegWeibull generate random deviates.
Within extreme value theory the reverse Weibull distibution (also known as the negative Weibull distribution) is often referred to as the Weibull distribution. We make a distinction to avoid confusion with the three-parameter distribution used in survival analysis, which is related by a change of sign to the distribution given above.
Alec Stephenson <alec_stephenson@hotmail.com>
dRevWeibull(-5:-3, -1, 0.5, 0.8) pRevWeibull(-5:-3, -1, 0.5, 0.8) qRevWeibull(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8) rRevWeibull(6, -1, 0.5, 0.8) p <- (1:9)/10 pRevWeibull(qRevWeibull(p, -1, 2, 0.8), -1, 2, 0.8) ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
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