The Excel NORMINV Function
The Normal distribution is a continuous probability function that is given by the formula:
where μ is the mean of the distribution, σ2 is the variance, and x is the independent variable for which you want to evaluate the function.
The Cumulative Normal Distribution function is given by the integral, from -∞ to x, of the Normal Probability Density function.
Further information on the Normal Distribution is provided on the Wikipedia Normal Distribution Page
NORMINV & NORM.INV Functions
In Excel 2010, the NORMINV function has been replaced by the NORM.INV function, which has improved accuracy.
Although it has been replaced, the Norminv function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.
The Excel NORMINV function calculates the inverse of the Cumulative Normal Distribution Function for a supplied value of x, and a supplied distribution mean & standard deviation.
The syntax of the function is:
NORMINV( probability, mean, standard_dev )
Where the function arguments are:
|probability||-||The value at which you want to evaluate the inverse function.|
|mean||-||The arithmetic mean of the distribution.|
|standard_dev||-||The standard deviation of the distribution.|
Excel uses an iterative method to calculate the Norminv function and seeks to find a result, x, such that:
( x, mean, standard_dev, TRUE ) = probability
Norminv Function Example
Inverse Normal Cumulative Distribution with mean = 5 & std. dev. = 2
The above chart on the right shows the Inverse Normal Cumulative Distribution Function with a Mean of 5 and a Standard Deviation of 2.
If you want to calculate the value of this function when the probability = 0.6, this can be done using the Excel Norminv function, as follows:
=NORMINV( 0.6, 5, 2 )
This gives the result 5.506694206.
For further information and examples of the Excel Norminv function, see the Microsoft Office website.
Norminv Function Errors
If you get an error from your Excel Norminv function this is likely to be one of the following:
Occurs if either:
- the supplied probability argument is < 0 or > 1
- the supplied standard_dev argument is ≤ 0.
|#VALUE!||-||Occurs if any of the supplied arguments is non-numeric.|