PoweR (version 1.0.7)

law0010.LogNormal: The Log Normal Distribution

Description

Random generation for the Log Normal distribution whose logarithm has mean equal to meanlog and standard deviation equal to sdlog.

This generator is called by function gensample to create random variables based on its parameters.

Details

If meanlog or sdlog are not specified they assume the default values of 0 and 1, respectively.

The Log Normal distribution has density: $$ \frac{1}{x\sigma\sqrt{2\pi}}e^{-\frac{(\ln x-\mu)^2}{2\sigma^2}} $$ where \(\mu\) and \(\sigma\) are the mean and standard deviation of the logarithm. The mean is \(E(X) = exp(\mu + 1/2 \sigma^2)\) and the variance is \(Var(X) = exp(2*\mu + \sigma^2)*(exp(\sigma^2) - 1)\).

References

Pierre Lafaye de Micheaux, Viet Anh Tran (2016). PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Studies for Goodness-of-fit Tests in R. Journal of Statistical Software, 69(3), 1--42. doi:10.18637/jss.v069.i03

See Also

Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(10,10000,law.pars=c(8,6))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }