Create a LogNormal distribution
LogNormal(log_mu = 0, log_sigma = 1)
log_mu |
The location parameter, written μ in textbooks.
Can be any real number. Defaults to |
log_sigma |
The scale parameter, written σ in textbooks.
Can be any positive real number. Defaults to |
We recommend reading this documentation on https://alexpghayes.github.io/distributions3, where the math will render with additional detail and much greater clarity.
In the following, let X be a LogNormal random variable with
success probability p = p.
Support: R^+
Mean: \exp(μ + σ^2/2)
Variance: [\exp(σ^2)-1]\exp(2μ+σ^2)
Probability density function (p.d.f):
f(x) = \frac{1}{xσ√{2π}}\exp(-\frac{(\log x - μ)^2}{2σ^2})
Cumulative distribution function (c.d.f):
F(x) = \frac{1}{2} + \frac{1}{2√{pi}}\int_{-x}^x e^{-t^2} dt
Moment generating function (m.g.f): Undefined.
A LogNormal object.
set.seed(27) X <- LogNormal(0.3, 2) X random(X, 10) pdf(X, 2) log_pdf(X, 2) cdf(X, 4) quantile(X, 0.7)
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