# Lognormal distribution

{*LOSnr43*}

### Merke

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{*LOSnr44*}
Determine the probability that a normally distributed random variable lies inside a given confidence interval.

If the natural logarithms lnX of a random variable X are normally distributed, we say that the random variable X is lognormally distributed. See fig. 7 for details.

Lognormal distribution

### Merke

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A lognormal distribution
- is bounded below by zero and
- is skewed to the right, i.e. it has a long right tail.

Therefore, observe the following.

### Methode

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• The lognormal distribution is an accurate description of the distribution of prices.
• The normal distribution is useful for approximating returns.

Memorize the expected mean and variance of a lognormal distribution:

 Distribution Mean Variance Normal distribution X ~ N(μ, σ2) μ σ2 Standard normal distribution N(0,1) 0 1 Lognormal distribution lnX μ0.5∙σ∙σ e2μ + σ∙σ∙(eσ∙σ - 1)

Tab. 9: Expected value and variance