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Unformatted text preview: McGill University Advanced Business Statistics MGSC272 MGSC 272 Lognormal Distribution The Lognormal Distribution A continuous random variable X follows a lognormal distribution if its natural logarithm, ln(X), follows a normal distribution. The lognormal distribution is an asymmetric distribution with interesting applications for modeling the probability distributions of stock and other asset prices The Lognormal Distribution Properties of the lognormal distribution The lognormal distribution is skewed to the right The lognormal distribution is strictly positive (i.e. bounded below by 0) The lognormal distribution may be used to model data on asset prices (note that prices are bounded below by 0) The Lognormal Distribution The lognormal distribution is described by two parameters, its mean and variance, as in the case of a normal distribution The mean of a lognormal distribution X is given by where and 2 are the mean and variance of the normal distribution of the ln( X ) variable and e 2.718 is the natural base for logarithms. ( 29 2 2 1 ) ( + = e X E The Lognormal Distribution The variance of a lognormal distribution is given by 2 2 (2 ) Var ( ) ( 1) X e e + = The Lognormal Distribution Observation Recall that the exponential and logarithmic functions are inverse functions This implies the following result...
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 Spring '12
 smith

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