6.11.2005

Q&A: For normal and lognormal distributions, list some of their similarities...

...as well as differences.

A

  • A random variable Y follows a lognormal distribution if its natural logarithm, lnY, is normally distributed.
    • The reverse is also true: if a random variable Y follows a lognormal distribution, then its natural logarithm, lnY, is normally distributed.
  • Like the normal distribution, the lognormal distribution is completely described by mean and variance. Unlike the normal distribution, the lognormal distribution is defined in terms of the parameters of the associated normal distribution.
    • In contrast, the normal distribution is defined by its own mean and variance. * the mean of Y is not equal to the mean of X, and the variance of Y is not equal to the variance of X.
  • The lognormal distribution is bounded below by 0. In contrast, the normal distribution extends to - infinite without limit.
  • The lognormal distribution is skewed to the right (that is, it has a long right tail). In contrast, the normal distribution is bell-shaped (i.e. it's symmetrical).

Category: Quantitative Analysis > Probability > Distribution

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