# Probability distributions in Excel 2007

These notes explain how to compute probabilities for common statistical distributions using Microsoft Excel 2007. See also notes on working with distributions in Mathematica, R and S-PLUS and in Python with SciPy.

Probability function support in Excel is incomplete and inconsistent. All distributions have a PDF function. Some have a CDF. Some have an inverse CDF. There’s a general pattern to function names, but there are exceptions.

Probability function names in Excel typically consist of a base name and a suffix. The base name is an abbreviation of the distribution name. The suffix is either `DIST` or `INV`. For example, the functions for the normal (Gaussian) distribution are `NORMDIST` and `NORMINV`. The corresponding functions for the Gamma distribution are `GAMMADIST` and `GAMMAINV`. Several distributions follow this pattern.

The “DIST” function evaluates the PDF and possibly the CDF. If the function has a `CUMULATIVE` argument, setting this argument to `TRUE` causes the `DIST` function to compute the CDF. If the argument is `FALSE`, the function returns the PDF. If there is no `CUMULATIVE` argument, the `DIST` function can only compute the PDF. The “INV” function evaluates the inverse CDF (quantile) function.

(By convention, Excel functions are written in all capital letters. That’s the way they are documented. But Excel is case-insensitive.)

Example:

The command to evaluate the PDF of a normal distribution with mean 1 and standard deviation 2 at the point x = 3 is

`NORMDIST(3, 1, 2, FALSE)`.

The `FALSE` argument says that the cumulative flag is not set. To compute the CDF of the same distribution at the point x = 3, the command is

`NORMDIST(3, 1, 2, TRUE)`.

To evaluate the inverse CDF (quantile function) of the distribution at p = 0.2 the command is

`NORMINV(0.2, 1, 2)`.

Not all distributions have an “INV” function, as indicated in the table below. Also, the lognormal distribution is exceptional in that its CDF inverse function is named `LOGINV` rather than `LOGNORMINV`.

For the Poisson and Weibull functions, the “DIST” function name does not end in “DIST.” Instead, these functions are `POISSON` and `WEIBULL`.

DistributionPDFCumulative?Quantile
Beta`BETADIST``BETAINV`
Bionomial`BINOMDIST`Yes`CRITBINOM`
Chi square`CHIDIST``CHIINV`
Exponential`EXPONDIST`Yes
F`FDIST``FINV`
Gamma`GAMMADIST`Yes`GAMMAINV`
Hypergeometric`HYPERGEOMDIST`
Log normal`LOGNORMDIST``LOGINV`
Negative binomial`NEGBINOMDIST`
Normal`NORMDIST`Yes`NORMINV`
Poisson`POISSON`Yes
Student t`TDIST``TINV`
Weibull`WEIBULL`Yes

The exponential distribution is parameterized in terms of its rate, the reciprocal of the mean. Other distributions that are sometimes parameterized differently are the hypergeometric and the lognormal.

For more details, see the Excel online documentation or statistical functions.