The key properties of the normal distribution have been presented in the LOS above. As a summary, some of the key properties of this distribution are:

- It is symmetrical about the mean.
- It has zero skewness.
- It has a kurtosis of 3.

A random variable, Y, follows a

- Like the normal distribution, the lognormal distribution is completely described by two parameters: mean and variance.
- Unlike the normal distribution, the lognormal distribution is defined in terms of the parameters of the associated normal distribution. Note that 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. In contrast, the normal distribution is defined by its own mean and variance.
- The lognormal distribution is bounded below by 0. In contrast, the normal distribution extends to negative infinity without limit.
- The lognormal distribution is skewed to the right (i.e., it has a long right tail). In contrast, the normal distribution is bell-shaped (i.e., it is symmetrical).

The reverse is also true; if a random variable Y follows a lognormal distribution, then its natural logarithm, lnY, is normally distributed.

rufi: this is a good tool for BSOPM |

bahodir: what is BSOPM? |

bobert: Black-Scholes Option Pricing Model |

Seemorr: What kind of variable would be lognormally distributed, but not normally? |

riouxcf: Some variables which have frequent outliers can be made more normal by taking the log. The normal distribution tends to underestimate extremes. |

czar: Seemor: stock prices (log) and stock returns (normal) as stock prices lowest value can only be 0 while returns can be negative |