- CFA Exams
- Level I 2020
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 10. The Lognormal Distribution

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##### Subject 10. The Lognormal Distribution PDF Download

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

**lognormal distribution**if its natural logarithm, lnY, is normally distributed. You can think of the term lognormal as "the log is normal." For example, suppose X is a normal random variable, and Y = e^{X}. Therefore, LnY = Ln(e^{X}) = X. Because X is normally distributed, Y follows a lognormal distribution.

- 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.

**Learning Outcome Statements**

CFA® Level I Curriculum, 2020, Volume 1, Reading 9

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**User Contributed Comments**
6

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Seemorr |
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