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Reference.org
Log-normal distribution
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<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, a log-normal (or lognormal) distribution is a continuous <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> of a <a href="/facts/Random_variable/TwTBXnLT">random variable</a> whose <a href="/facts/Logarithm/QeXaV97q">logarithm</a> is <a href="/facts/Normal_distribution/UapjjPyQ">normally distributed</a>. Thus, if the random variable X is log-normally distributed, then <i>Y</i> = ln(<i>X</i>) has a normal distribution. Equivalently, if Y has a normal distribution, then the <a href="/facts/Exponential_function/ewlYxvR2">exponential function</a> of Y, <i>X</i> = exp(<i>Y</i>) , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and <a href="/facts/Engineering/RFVg8H3I">engineering</a> sciences, as well as <a href="/facts/Medicine/2fnp90Je">medicine</a>, <a href="/facts/Economics/HYctA2Dn">economics</a> and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). </p><p>The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after <a href="/facts/Francis_Galton/9Hu0Ex1R">Francis Galton</a>. The log-normal distribution has also been associated with other names, such as <a href="/facts/Donald_MacAlister/bQbscrVj">McAlister</a>, <a href="/facts/Gibrat%27s_law/pCWFV3IE">Gibrat</a> and <a href="/facts/Cobb%E2%80%93Douglas/qwFIucgW">Cobb–Douglas</a>. </p><p>A log-normal process is the statistical realization of the multiplicative <a href="/facts/Mathematical_product/aXY11nGS">product</a> of many <a href="/facts/Statistical_independence/NUzQtnUL">independent</a> <a href="/facts/Random_variable/TwTBXnLT">random variables</a>, each of which is positive. This is justified by considering the <a href="/facts/Central_limit_theorem/0gc2L0Wd">central limit theorem</a> in the log domain (sometimes called <a href="/facts/Gibrat%27s_law/pCWFV3IE">Gibrat's law</a>). The log-normal distribution is the <a href="/facts/Maximum_entropy_probability_distribution/MVwFzu49">maximum entropy probability distribution</a> for a random variate X—for which the mean and variance of ln(<i>X</i>) are specified. </p>