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Log norm dist

LOGNORMDIST Function

The LOGNORMDIST function in Excel is used to return the cumulative lognormal distribution of a value x. The lognormal distribution describes a continuous distribution of a random variable whose natural logarithm is normally distributed. This function is often used in financial modeling and risk analysis.

Syntax

LOGNORMDIST(x, mean, standard_dev)

Parameters

  • x: The value at which to evaluate the function. This must be a positive number.
  • mean: The mean of the natural logarithm of the distribution.
  • standard_dev: The standard deviation of the natural logarithm of the distribution. This must be a positive number.

Notes

  • If x is ≤ 0, or if standard_dev ≤ 0, the function will return an error.
  • The cumulative distribution function (CDF) is calculated as:
    [ \text{LOGNORMDIST}(x) = \frac{1}{x \cdot \sigma \cdot \sqrt{2\pi}} e^{-\frac{(\ln(x) - \mu)^2}{2\sigma^2}} ] Where:
    • ( x ) is the input value.
    • ( \mu ) is the mean of the natural logarithm of the distribution (mean).
    • ( \sigma ) is the standard deviation of the natural logarithm of the distribution (standard_dev).

Deprecation

In recent versions of Excel (2010 and later), the LOGNORMDIST function has been replaced with LOGNORM.DIST. The newer version provides more precise control over cumulative vs. probability density functions:

  • Use LOGNORM.DIST for newer models to specify cumulative (TRUE) or probability density (FALSE) explicitly using an additional argument.

Example

=LOGNORMDIST(4, 3.5, 1.2)

This returns the cumulative lognormal distribution of the value 4 with a mean of 3.5 and a standard deviation of 1.2.