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Update the FAQ vignette: attempt to make the equations executable
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aursiber committed Aug 28, 2024
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Expand Up @@ -95,9 +95,10 @@ summary(fendo.B)
## Why there are differences between MLE and MME for the lognormal distribution?
We recall that the lognormal distribution function is given by

$$
F_X(x) = \Phi\left(\frac{\log(x)-\mu}{\sigma} \right),
$$

$$f(x) = \dfrac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(x-\mu^2)}{2\sigma^2}}$$

$$F_X(x) = \Phi\left(\frac{\log(x)-\mu}{\sigma} \right),$$

where $\Phi$ denotes the distribution function of the standard normal distribution.
We know that $E(X) = \exp\left( \mu+\frac{1}{2} \sigma^2 \right)$
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