What is Log-Normal Distribution

The log-normal distribution is a term associated with statistics and probability theory. Similarly, another name for the log-normal distribution is Galton distribution. The log-normal distribution represents a continuous distribution of random variables with normally distributed logarithms. It follows the concept that instead of having normally distributed original data, the logarithms of the data also show normal distribution.

A log-normal distribution is similar to normal distribution. In fact, the data in both of them can be used interchangeably by calculating the logarithms of the data points. However, the log-normal distribution is different from the normal distribution in many ways.

The biggest differentiating factor between the two is their shapes. While normal distribution represents a symmetrical shape, a log-normal distribution does not. The difference in their shapes comes due to their skewness. As log-normal distribution uses logarithmic values, the values are positive, thus, creating a right-skewed curve. Another difference between the two is the values used on deriving both.

What are the parameters of Log-normal Distribution?

The log-normal distribution has three parameters. These are the median, the location, and the standard deviation. Firstly, the median, also known as the scale, parameter, shrinks, or stretches the graph, represented by ‘m’. Secondly, the location, represented by ‘Θ’ or ‘μ’ represents the x-axis location of the graph.

Lastly, the shape parameter or standard deviation, represented by ‘σ’, affects the overall shape of the log-normal distribution. It does not impact the location or height of the graph. The parameters are available in historical data. However, it is also possible to estimate using current data.

What are the characteristics of Log-normal distribution?

Log-normal distribution has several characteristics or features. First of all, it shows a positive skew towards the right due to its lower mean values and higher variances in the random variables in consideration. Secondly, for log-normal distribution, the mean is usually higher than its mode because of its skew with a large number of small values and few major values.

Lastly, log-normal distribution does not include negative values. It is a feature that differentiates it from a normal distribution and, therefore, a defining characteristic.

What are the uses of Log-normal distribution?

Log-normal has several use cases in the world of finance. Most importantly, it fixes some problems with normal distribution, which helps increase its usage. For example, a normal distribution may include negative variables, while log-normal distribution consists of positive variables only. Apart from that, log-normal distribution is also commonly used in stock prices analysis.

Log-normal distribution can help investors identify the compound return that they can expect from a stock over a period of time. Usually, they use the normal distribution to analyze the potential returns they get from it. However, for analyzing the prices of stocks, log-normal is a better choice.

In finance, log-normal distribution common for calculating asset price over a period of time. It is because normal distribution may provide inconsistent prices, while log-normal does not have the same problem. It solves the problem with normal distribution taking asset prices below zero or negative. Therefore, the log-normal produces better results.


The log-normal distribution shows the continuous distribution of random variables with normally distributed logarithmic values. It is different from the normal distribution in several ways. There are three parameters in log-normal distribution, the median, the location, and the standard deviation.

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