Description Usage Arguments Details Value Examples
Raw moments for the Lognormal distribution.
1 |
r |
rth raw moment of the distribution, defaults to 1. |
truncation |
lower truncation parameter, defaults to 0. |
meanlog, sdlog |
mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively. |
lower.tail |
logical; if TRUE (default), moments are E[x^r|X ≤ y], otherwise, E[x^r|X > y] |
Probability and Cumulative Distribution Function:
f(x) = \frac{1}{{x Var √ {2π } }}e^{- (lnx - μ )^2/ 2Var^2} , \qquad F_X(x) = Φ(\frac{lnx- μ}{Var})
The y-bounded r-th raw moment of the Lognormal distribution equals:
μ^r_y = e^{\frac{r (rVar^2 + 2μ)}{2}}[1-Φ(\frac{lny - (rVar^2 + μ)}{Var})]
Provides the y-bounded, rth raw moment of the distribution.
1 2 3 4 5 6 7 8 9 10 11 12 | ## The zeroth truncated moment is equivalent to the probability function
plnorm(2, meanlog = -0.5, sdlog = 0.5)
mlnorm(truncation = 2)
## The (truncated) first moment is equivalent to the mean of a (truncated) random sample,
#for large enough samples.
x <- rlnorm(1e5, meanlog = -0.5, sdlog = 0.5)
mean(x)
mlnorm(r = 1, lower.tail = FALSE)
sum(x[x > quantile(x, 0.1)]) / length(x)
mlnorm(r = 1, truncation = quantile(x, 0.1), lower.tail = FALSE)
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