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!set gl_author=Sophie, Lemaire
!set gl_keywords=continuous_probability_distribution
!set gl_title=
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<div class="wims_defn"><h4>Definition</h4>
Let \(m) be a real and let \(s) be a positive real.
The <span class="wims_emph">log-normal distribution with
parameters \(m) and \(s)</span> (denoted by
\(\mathcal{LN}(m,s))) is the distribution of the random variable
\(exp(X)) where \(X) has the \(\mathcal{N}(m,s^2)) distribution. The
density function of \(\mathcal{L N}(m,s)) is

<div class="wimscenter">
\( x \mapsto \frac{1}{sx\sqrt{2\pi}}exp(-\frac{(\log(x)-m)^2}{2s^2})1_{x>0})
</div>
</div>
<table class="wimsborder wimscenter">
<tr><th>Expectation</th><th>Variance</th><th>Characteristic function</th></tr>
<td>\(\exp(m+\frac{s^2}{2}))</td><td>\((\exp(s^2)-1)\exp(2m+s^2))</td><td></td></tr></table>
