Probability Distribution- Lognormal

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Lognormal Distribution: As per probability distribution theory, a log-normal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. In other words, a lognormal distribution is generated by the function ex, where x is normally distributed. The natural logarithm (ln) of ex is x, which is normally distributed and accordingly the name given.

The Probability density function for lognormal distribution is:

Log_Nor_Distri111

Lognormal vs Normal Distribution:

Log_Nor_Distri112

Few Important properties of Lognormal Distribution:

  1. Lognormal Distribution is skewed to the right
  2. Lognormal Distribution is bounded from below by zero, so this distribution is very helpful in modeling asset prices which cannot take values less than zero, in case we use normal distribution we admit that prices of asset can be negative which practically is not possible

 

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