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Reference.org
Exponentially modified Gaussian distribution
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<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent <a href="/facts/Normal_distribution/UapjjPyQ">normal</a> and <a href="/facts/Exponential_distribution/yY3EdV0u">exponential</a> random variables. An exGaussian random variable <i>Z</i> may be expressed as <i>Z</i> = <i>X</i> + <i>Y</i>, where <i>X</i> and <i>Y</i> are independent, <i>X</i> is Gaussian with mean <i>μ</i> and variance <i>σ</i>2, and <i>Y</i> is exponential of rate <i>λ</i>. It has a characteristic positive skew from the exponential component. </p><p>It may also be regarded as a weighted function of a shifted exponential with the weight being a function of the normal distribution. </p>