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!set gl_author=Sophie, Lemaire
!set gl_keywords=continuous_probability_distribution
!set gl_title=Gamma distribution
!set gl_level=U1,U2,U3
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<div class="wims_defn"><h4>Definition</h4>
Let \(a) and \(b) be two positive numbers. The <strong>Gamma distribution</strong>
  with parameters \(a) and \(b) (denoted by \(Gamma(a,b))) is a continuous distribution over
  \(\RR_+) with density function

<div class="wimscenter">
 \(x\mapsto\frac{b^a e^{-b x}x^{a-1}}{\Gamma(a) }1_{x>0})
</div>
</div>
<table class="wimsborder wimscenter">
<tr><th>Expectation</th><th>Variance</th><th>Characteristic function</th></tr>
<td>\(\frac{a}{b})</td><td>\(\frac{a}{b^2})</td><td>\((1-\frac{i t}{b})^{-a})</td></tr></table>

<p>
If \(a) is a positive integer, \(Gamma(a,b)) is the distribution of the sum of \(a)
independent random variables exponentially distributed with parameter \(b).
</p>


