# Defining Normal Distribution in Commercial Real Estate

Have you ever seen a bell curve before? Well, that is the graph form of normal distribution.

## What Is Normal Distribution?

Normal distribution is a probability distribution that shows data near the mean is more frequent than data outside of the mean. Hence why it appears as a bell curve when in graph form.

All normal distributions are symmetrical. However, not all symmetrical distributions are normal distributions.

Normal distribution has two parameters: the mean and standard deviation. It is important to keep these figures in mind when determining if something fits normal distribution:

68% of observations are within (+/-) one standard deviation of the mean

95% of observations are within (+/-) two standard deviations of the mean

99.7% of observations are within (+/-) three standard deviations of the mean.

Applying the above will help you from confusing normal distribution from symmetrical distribution. Symmetrical distribution is where there is mirrored distribution on either side of a dividing line — this could be a series of humps rather than the singular bell curve of normal distribution.

Data in real life very rarely follows perfect normal distribution. The skewness and kurtosis coefficients calculate how dissimilar a distribution is from perfect normal distribution.

Skewness calculates how symmetrical a distribution is. Perfect normal distribution has a skewness of zero — meaning it is symmetrical. When a distribution has negative skewness (less than zero), the left tail will be longer than the right tail. When a distribution has a positive skewness (more than zero), the right tail will be longer than the left tail.

Kurtosis calculates how thick the tail ends of a distribution are. Normal distribution has a kurtosis of three.

When the kurtosis has a value above three (large kurtosis), tail data will surpass the tails of normal distribution (heavy tails). When the kurtosis has a value below three (low kurtosis), tail data will be shorter than those of normal distribution (thin tails).

## How Does This Apply to Commercial Real Estate Finance?

In finance, normal distribution is used on asset prices as well as price action. This data allows investors to decide if an asset is being over or undervalued. It may also be used during a commercial real estate appraisal.

When it comes to commercial real estate, this distribution will show what income the property is producing. Many real estate researches have assumed that real estate returns are normally distributed and have finite variance.

Nonetheless, there are some researchers who strongly reject the use of normal distribution when it comes to commercial real estate, after evidence was found of time-varying heteroscedasticity and skewness.