Laplace distribution
Density, distribution function, quantile function and random generation for the Laplace distribution.
dlaplace(x, mu = 0, sigma = 1, log = FALSE) plaplace(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qlaplace(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rlaplace(n, mu = 0, sigma = 1)
x, q |
vector of quantiles. |
mu, sigma |
location and scale parameters. Scale must be positive. |
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]. |
p |
vector of probabilities. |
n |
number of observations. If |
Probability density function
f(x) = 1/(2*σ) * exp(-|(x-μ)/σ|)
Cumulative distribution function
F(x) = [if x < mu:] 1/2 * exp((x-μ)/σ) [else:] 1 - 1/2 * exp((x-μ)/σ)
Quantile function
F^-1(p) = [if p < 0.5:] μ + σ * log(2*p) [else:] μ - σ * log(2*(1-p))
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC
Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.
x <- rlaplace(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dlaplace(x, 5, 16), -200, 200, n = 500, col = "red", add = TRUE) hist(plaplace(x, 5, 16)) plot(ecdf(x)) curve(plaplace(x, 5, 16), -200, 200, n = 500, col = "red", lwd = 2, add = TRUE)
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