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Reference.org
Logit-normal distribution
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<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, a logit-normal distribution is a <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> of a <a href="/facts/Random_variable/TwTBXnLT">random variable</a> whose <a href="/facts/Logit/5674C2DL">logit</a> has a <a href="/facts/Normal_distribution/UapjjPyQ">normal distribution</a>. If <i>Y</i> is a random variable with a normal distribution, and <i>t</i> is the standard <a href="/facts/Logistic_function/IaQ254t7">logistic function</a>, then <i>X</i> = <i>t</i>(<i>Y</i>) has a logit-normal distribution; likewise, if <i>X</i> is logit-normally distributed, then <i>Y</i> = <a href="/facts/Logit/5674C2DL">logit</a>(<i>X</i>)= log (<i>X</i>/(1-<i>X</i>)) is normally distributed. It is also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.). </p><p>A variable might be modeled as logit-normal if it is a proportion, which is bounded by zero and one, and where values of zero and one never occur. </p>