In mathematics, the error function (also called the Gauss error function or ERF) is a special, non-elementary function that occurs in probability, statistics and partial differential equations describing diffusion. It is defined as:
In statistics, for nonnegative values of x, the error function has the following interpretation: for a random variable Y that is normally distributed with mean 0 and variance 1/2, ERF(x) describes the probability of Y falling in the range [−x, x]. This function returns the error function integrated between lower_limit and upper_limit.
The ERF function syntax has the following arguments:
- Lower_limit Required. The lower bound for integrating ERF.
Upper_limit Optional. The upper bound for integrating ERF. If omitted, ERF integrates between zero and lower_limit.
Example: Let’s look at some Excel ERF function examples and explore how to use the ERF function as a worksheet function in Microsoft Excel:
Based on the Excel spreadsheet above, the following ERF examples would return:
- If lower_limit is nonnumeric, ERF returns the #VALUE! error value.
- If upper_limit is nonnumeric, ERF returns the #VALUE! error value