Gumbel: The Gumbel distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the Gumbel distribution with location parameter mu and scale parameter sigma.

Usage

dgumbel(x, mu, sigma, log = FALSE)
pgumbel(q, mu, sigma, lower.tail = TRUE, log.p = FALSE)
qgumbel(p, mu, sigma, lower.tail = TRUE, log.p = FALSE)
rgumbel(n, mu, sigma)

Arguments

x,q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
mu	location parameter.
sigma	scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].

Details

The Gumbel distribution has density

f(x) = 1/σ exp{-((x-μ)/σ)} exp[-exp{-((x-μ)/σ)}]; -∞ < x < ∞, σ > 0.

where μ and σ are the shape and scale parameters, respectively.

Value

dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and rgumbel generates random deviates.

References

Marshall, A. W., Olkin, I. (2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families, Springer, New York.

See Also

.Random.seed about random number; sgumbel for Gumbel survival / hazard etc. functions

Examples

## Load data sets
data(dataset2)
## Maximum Likelihood(ML) Estimates of mu & sigma for the data(dataset2)
## Estimates of mu & sigma using 'maxLik' package
## mu.est = 212.157, sigma.est = 151.768

dgumbel(dataset2, 212.157, 151.768, log = FALSE)
pgumbel(dataset2, 212.157, 151.768, lower.tail = TRUE, log.p = FALSE)
qgumbel(0.25, 212.157, 151.768, lower.tail=TRUE, log.p = FALSE)
rgumbel(30, 212.157, 151.768)

Example output

  [1] 5.857709e-04 6.179121e-04 7.663393e-04 9.018112e-04 1.083492e-03
  [6] 1.083492e-03 1.176692e-03 1.176692e-03 1.176692e-03 1.216869e-03
 [11] 1.283934e-03 1.283934e-03 1.470349e-03 1.587145e-03 1.662836e-03
 [16] 1.662836e-03 1.724250e-03 1.736331e-03 1.736331e-03 1.748340e-03
 [21] 1.760277e-03 1.807265e-03 1.807265e-03 1.852966e-03 1.981457e-03
 [26] 1.991536e-03 2.040378e-03 2.255642e-03 2.297257e-03 2.302712e-03
 [31] 2.302712e-03 2.337453e-03 2.376686e-03 2.394433e-03 2.403894e-03
 [36] 2.405966e-03 2.418414e-03 2.420397e-03 2.423781e-03 2.409612e-03
 [41] 2.407898e-03 2.397970e-03 2.397970e-03 2.393381e-03 2.390957e-03
 [46] 2.390957e-03 2.388448e-03 2.377579e-03 2.352020e-03 2.344875e-03
 [51] 2.329725e-03 2.317639e-03 2.304959e-03 2.291707e-03 2.282567e-03
 [56] 2.268414e-03 2.268414e-03 2.263582e-03 2.253752e-03 2.228242e-03
 [61] 2.201483e-03 2.179244e-03 2.179244e-03 2.162112e-03 2.150488e-03
 [66] 2.114706e-03 2.077686e-03 2.058760e-03 1.960725e-03 1.960725e-03
 [71] 1.933805e-03 1.927034e-03 1.892963e-03 1.872368e-03 1.796142e-03
 [76] 1.782198e-03 1.642438e-03 1.504302e-03 1.483888e-03 1.477106e-03
 [81] 1.396694e-03 1.363777e-03 1.357239e-03 1.357239e-03 1.318343e-03
 [86] 1.205356e-03 1.205356e-03 1.205356e-03 1.205356e-03 1.169023e-03
 [91] 1.169023e-03 1.098484e-03 1.019906e-03 1.014450e-03 9.097779e-04
 [96] 8.090175e-04 7.953815e-04 7.730710e-04 6.091019e-04 6.055088e-04
[101] 5.571242e-04 5.122010e-04 3.612723e-04 3.612723e-04 3.373820e-04
[106] 2.129070e-04 2.049194e-04 1.637950e-04 1.496975e-04 3.793220e-05
[111] 2.396776e-05
  [1] 0.02377635 0.02558166 0.03456396 0.04373159 0.05761922 0.05761922
  [7] 0.06552929 0.06552929 0.06552929 0.06911961 0.07537161 0.07537161
 [13] 0.09465583 0.10841709 0.11816803 0.11816803 0.12663643 0.12836672
 [19] 0.12836672 0.13010906 0.13186338 0.13899888 0.13899888 0.14631978
 [25] 0.16933985 0.17132636 0.18140723 0.23959429 0.25553294 0.25783293
 [31] 0.25783293 0.27407702 0.29765785 0.31197336 0.32157064 0.32397558
 [37] 0.34327796 0.34811685 0.37234669 0.40862480 0.41103356 0.42304917
 [43] 0.42304917 0.42784058 0.43023275 0.43023275 0.43262246 0.44215496
 [49] 0.46107665 0.46577359 0.47512317 0.48209437 0.48902841 0.49592355
 [55] 0.50049786 0.50732446 0.50732446 0.50959047 0.51410784 0.52531336
 [61] 0.53638818 0.54514987 0.54514987 0.55166200 0.55597462 0.56877086
 [67] 0.58134862 0.58755335 0.61770594 0.61770594 0.62549509 0.62742551
 [73] 0.63697565 0.64262367 0.66280134 0.66637968 0.70062586 0.73208821
 [79] 0.73657047 0.73805096 0.75529188 0.76219290 0.76355341 0.76355341
 [85] 0.77157987 0.79428449 0.79428449 0.79428449 0.79428449 0.80140728
 [91] 0.80140728 0.81500944 0.82983342 0.83085060 0.85007871 0.86810973
 [97] 0.87051628 0.87443720 0.90265847 0.90326577 0.91140006 0.91888140
[103] 0.94354603 0.94354603 0.94738723 0.96714168 0.96839501 0.97482149
[109] 0.97701449 0.99422641 0.99635581
[1] 162.5844
 [1] 224.9391 198.0617 318.2065 558.9326 270.0975 323.8690 270.7704 584.2396
 [9] 387.2082 422.5231 309.9068 434.7736 302.6197 417.2671 472.7893 350.4709
[17] 325.9925 208.1814 171.6237 753.7436 515.8345 139.3581 348.6394 166.0847
[25] 112.2362 116.1671 208.0581 170.3887 301.5284 165.4344

reliaR documentation built on May 1, 2019, 9:51 p.m.