LogNormal | R Documentation |
A random variable created by exponentiating a Normal()
distribution. Taking the log of LogNormal data returns in
Normal()
data.
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}{x σ √{2 π}} \exp (-\frac{(\log x - μ)^2}{2 σ^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.
Other continuous distributions:
Beta()
,
Cauchy()
,
ChiSquare()
,
Erlang()
,
Exponential()
,
FisherF()
,
Frechet()
,
GEV()
,
GP()
,
Gamma()
,
Gumbel()
,
Logistic()
,
Normal()
,
RevWeibull()
,
StudentsT()
,
Tukey()
,
Uniform()
,
Weibull()
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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