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Density function, distribution function, and quantile function for the Lognormal distribution.
plnorm3(q, meanlog, sdlog, threshold)
dlnorm3 gives the density, plnorm3 gives the distribution function, and qlnorm3 gives the quantile function.
dlnorm3
plnorm3
qlnorm3
A numeric vector of quantiles.
The mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.
0
1
The threshold parameter, default is 0.
The Lognormal distribution with meanlog parameter zeta, sdlog parameter sigma, and threshold parameter theta has a density given by:
meanlog
sdlog
threshold
$$f(x) = \frac{1}{\sqrt{2\pi}\sigma(x-\theta)}\exp\left(-\frac{(\log(x-\theta)-\zeta)^2}{2\sigma^2}\right)$$
The cumulative distribution function is given by:
$$F(x) = \Phi\left(\frac{\log(x-\theta)-\zeta}{\sigma}\right)$$
where \(\Phi\) is the cumulative distribution function of the standard normal distribution.
dlnorm3(x = 2, meanlog = 0, sdlog = 1/8, threshold = 1) temp <- plnorm3(q = 2, meanlog = 0, sdlog = 1/8, threshold = 1) temp qlnorm3(p = temp, meanlog = 0, sdlog = 1/8, threshold = 1)
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