The Gumbel Distribution
Density, distribution function, quantile function and random generation for the Gumbel distribution with location and scale parameters.
dgumbel(x, loc, scale, log = FALSE) pgumbel(q, loc, scale, lower.tail = TRUE, log.p = FALSE) qgumbel(p, loc, scale, lower.tail = TRUE, log.p = FALSE) rgumbel(n, loc, scale)
x, q |
vector of quantiles. |
loc |
location parameter. |
scale |
scale parameter. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p), default: FALSE. |
lower.tail |
logical; if TRUE, probabilities are P[X ≤ x] otherwise, P[X > x], default: TRUE. |
p |
vector of probabilities. |
n |
number of observations. |
The Gumbel distribution function with location parameter μ and scale parameter β has density given by
f(x)=1/β e^-(z+e^-z)
, where z=(x-μ)/β. The cumulative distribution function is
F(x)=e^(-e^z)
with z as stated above.
See https://en.wikipedia.org/wiki/Gumbel_distribution for more details.
dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and
rgumbel generates random deviates.
Invalid arguments will result in return value NaN, with a warning.
dgumbel(seq(1, 5), 0, 1) qgumbel(pgumbel(seq(1, 5), 0, 1), 0 ,1) rgumbel(5, 0, 1)
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