Wald (inverse Gaussian) distribution
Density, distribution function and random generation for the Wald distribution.
dwald(x, mu, lambda, log = FALSE) pwald(q, mu, lambda, lower.tail = TRUE, log.p = FALSE) rwald(n, mu, lambda)
x, q |
vector of quantiles. |
mu, lambda |
location and shape 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]. |
n |
number of observations. If |
p |
vector of probabilities. |
Probability density function
f(x) = sqrt(λ/(2*π*x^3)) * exp((-λ*(x-μ)^2)/(2*μ^2*x))
Cumulative distribution function
F(x) = Φ(sqrt(λ/μ)*(x/μ-1)) - exp((2*λ)/μ) * Φ(sqrt(λ/μ)*(x/μ+1))
Random generation is done using the algorithm described by Michael, Schucany and Haas (1976).
Michael, J.R., Schucany, W.R., and Haas, R.W. (1976). Generating Random Variates Using Transformations with Multiple Roots. The American Statistician, 30(2): 88-90.
x <- rwald(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dwald(x, 5, 16), 0, 50, col = "red", add = TRUE) hist(pwald(x, 5, 16)) plot(ecdf(x)) curve(pwald(x, 5, 16), 0, 50, col = "red", lwd = 2, add = TRUE)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.