The LOGNORMDIST function in Excel is a powerful statistical tool used to compute the cumulative density function of a lognormal distribution. A lognormal distribution is significant in various fields, including finance and environmental studies, where data sets are positively skewed. This function allows analysts to determine the probability that a random variable following a lognormal distribution will be less than or equal to a specified value.

Syntax

LOGNORMDIST(x, mean, standard_dev, cumulative)

• x: The value for which you want the function to evaluate the cumulative lognormal distribution.
• mean: The arithmetic mean of the natural logarithm of the distribution.
• standard_dev: The standard deviation of the natural logarithm of the distribution.
• cumulative: A logical value that determines the form of the function. Use TRUE for the cumulative distribution function, and FALSE for the probability density function.

Example #1

=LOGNORMDIST(2, 0, 1, TRUE)

This function calculates the cumulative lognormal distribution for 2 with a mean of 0 and a standard deviation of 1. The result is approximately 0.8413, indicating that there is an 84.13% probability that a value is less than or equal to 2.

Example #2

=LOGNORMDIST(4, 1, 0.5, TRUE)

In this example, the function evaluates the cumulative lognormal distribution for 4 with a mean of 1 and a standard deviation of 0.5. The result is around 0.9820, signifying a 98.20% probability that the variable will be less than or equal to 4.

Example #3

=LOGNORMDIST(1, 0.5, 0.75, FALSE)

This function calculates the probability density function for a value of 1, with a mean of 0.5 and a standard deviation of 0.75. The result is approximately 0.2593, which reflects the density of the value 1 in the lognormal distribution.

Error handling

• NUM!: Occurs when the mean is less than or equal to 0. This indicates that the inputs do not define a valid lognormal distribution.
• VALUE!: Appears if any of the parameters are of the wrong type, such as a text string instead of a numeric value.
• N/A: Indicates that the result cannot be computed due to invalid parameters.

Conclusion

The LOGNORMDIST function is an essential tool for statistical analysis in Excel, providing users with valuable insights into lognormally distributed data. By mastering its syntax and understanding its applications, one can effectively assess probabilities and make data-driven decisions based on the characteristics of the distributions at hand.