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 SPLUS 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 caseinsensitive.)
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
.
Distribution  Cumulative?  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.
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