Arrays are shown in curly brackets {.,.,.}. They must be input as a list, e.g. {1,2,3..} or a range name, or an array reference e.g. A1:A4.
Note that many of the statistical functions below are written for compatibility with earlier versions of EXCEL. For example, NORMDIST() is now NORM.DIST(). The arguments are for the most part the same and both versions of the formula exist in the newer versions of EXCEL, but it's better to use the latest versions (i.e. with a period in the formula name) as they are more accurate.
Descriptive Statistics
These functions provide basic statistical values for data sets and are useful for analyzing data, or the exported results of simulations.
AVERAGE
AVERAGE({x}) returns the mean of a data set
COVAR
COVAR({x},{y}) returns the covariance between data sets {x} and {y}.
FREQUENCY
FREQUENCY({x},{bins}) is an array function that counts the number of data points in the data set {x} that are in each bin. You have to be careful of how the function behaves at the ends of the bin array.
KURT
KURT({x}) + 3 returns the kurtosis of a data set
MAX
MAX({x}) returns the maximum of a data set
MEDIAN
MEDIAN({x}) returns the median of a data set
MIN
MIN({x}) returns the minimum of a data set
MULTINOMIAL
MULTINOMIAL({s}) returns the multinomial coefficient

for which the binomial coefficient COMBIN is a special case.
PERCENTILE
PERCENTILE(array,k) returns the k-th percentile of values in a range. You can use this function to establish a threshold of acceptance. For example, you can decide to examine candidates who score above the 90th percentile.
RANK
Rank =RANK(x,array,order) order: 0=descending; 1=ascending
SKEW
SKEW({x}) returns the skewness of a data set
VAR
VAR({x}) returns the variance of a data set
Distributions
Returns a value (given the probability) or a probability (give the value) from a probability distribution, NOT a random value like Crystal Ball distributions. The parameter cumulative allows you to control whether the returned probability is from the probability mass (or probability density curve), or from the cumulative probability curve.
BETADIST
BETADIST(x,a,b,min,max) returns the cumulative probability of x from the Beta(a, b) distribution. If the min and max optional parameters are used, it rescales the beta distribution.
BETAINV
BETAINV(P,a,b,min,max) returns the cumulative percentile xP from a Beta(a,b) distribution. If the min and max optional parameters are used, it rescales the beta distribution.
BINOMDIST
BINOMDIST(x,n,p,cumulative) returns the probabilities of x from the Binomial(n,p) distribution.
EXPONDIST
EXPONDIST(x,l,cumulative) returns the probabilities of x from the Expon(b) distribution where l = 1/b. (the departure from standard convention for the parameter can be confusing, and is inconsistent with the GAMMADIST function, so be careful)
GAMMADIST
GAMMADIST(x,a,b,cumulative) returns the probabilities of x from the Gamma(a,b) distribution.
HYPGEOMDIST
HYPGEOMDIST(x,n,D,M) returns the probability mass of x from the Hypergeometric(n,D,M) distribution.
LOGINV
LOGINV(P,m,s) returns the cumulative percentile xP from a Lognorm2(m,s) distribution (i.e. the mean and standard deviation apply to the corresponding Normal distribution.
LOGNORMDIST
LOGNORMDIST(x,m,s) returns the cumulative probability from a Lognorm2(m,s) distribution (i.e. the mean and standard deviation apply to the corresponding Normal distribution.
NORMDIST
NORMDIST(x,m,s,cumulative) returns the probabilities of x from the Normal(m,s) distribution.
NORMSINV
NORMSINV(P) returns the cumulative percentile xP from a standard Normal distribution Normal(0,1).
POISSON
POISSON(x,l, cumulative) returns the probabilities of x from the Poisson(l) distribution.
TDIST
Returns the Percentage Points (probability) for the Student t-distribution where a numeric value (x) is a calculated value of t for which the Percentage Points are to be computed. The t-distribution is used in the hypothesis testing of small sample data sets.
WEIBULL
WEIBULL(x,a,b,cumulative) returns the probabilities of x from a Weibull(a,b) distribution.
Least Squares Regression
These functions return statistical parameters or projections from a least squares regression that attempts to fit an equation that relates the independent variable X to the dependent variable Y as follows:
Y = Normal(m*X+c,Syx)
The {x} array is the set of observations for independent variable X, and the {y} array is the set of observations for the dependent variable Y
INTERCEPT
INTERCEPT({y},{x}) returns the estimated c
SLOPE
SLOPE({y},{x}) returns the estimated m
STEYX
TREND({y},{x},new-xs,constant) returns an array of y-values corresponding to the new x-values, after attempting a regression fit on {y}, {x}. For example:

The Excel function FORECAST serves the same purpose.
General
These functions perform basic operations on cells, look up values in data tables, and perform logical tests which are the basic building blocks of risk analysis modeling.
ABS
ABS(x) returns the absolute value of x, so:
ABS(-4) = 4, ABS(4) = 4.
AND
AND(condition1, condition2,&) returns a TRUE if al conditions are met, and a false otherwise. For example:
A1: 10
A2: 12
A3: 6
=AND(A1>=10, A3>2*A1,A2>=2*A3) returns a TRUE
=AND(A1>=10, A3>2*A1,A2>2*A3) returns a FALSE
CONCATENATE
CONCATENATE (text1,text2,...) joins several text strings into one text string.
COUNT
COUNT({x}) counts the number of cells that contain numbers and also numbers within the list of arguments. Use COUNT to get the number of entries in a number field that's in a range or array of numbers.
COUNTIF
COUNTIF({x},criterion) counts how many cells in the range that {x} satisfy the criterion.
EXP
EXP(x) returns the natural exponent of x, i.e. ex.
FACT
FACT(x) returns the factorial of x, i.e. 1*2*&*x. For example:
FACT(4) = 12
FACT(1) = 1
FACT(0) = 1 That might surprise you its a strange result that comes from the gamma function definition of a factorial:
FACT rounds x to the nearest value, but mathematically you can have a factorial of any positive real number. If you want the factorial of say 3.3, you can write:
= EXP(GAMMALN(3.3+1)) = EXP(GAMMALN(4.3))
For any non-negative integer:
FACT(x) = EXP(GAMMALN(x+1))
FALSE
FALSE( ) returns the logical value FALSE.
GAMMALN
GAMMALN(x) returns the log of the gamma function of x. Actually, this IS useful though rather esoteric, as several probability distributions contain a gamma function. It is also an alternative to calculating very large factorial:
= GAMMALN(n+1)
So this function is closely related to Excels FACT function.
HLOOKUP
HLOOKUP(v,A,i) looks up in a table delineated by the area A. It searches for the value v in the first row, and then returns the value in the ith row of the same column. For example:

This is a useful function in combination with a probability distribution for selecting random or conditional values from tables. However, it can be somewhat tricky in predicting what it will do at the end of tables, and wont work properly unless the first column is put in ascending order. For these reasons we tend to use the functions OFFSET and INDEX for this purpose.
IF
IF(condition,A,B) returns the value A if the condition is true, and the value B otherwise. For example:
A1: 10
A2: 12
A3: 6
=IF(A1>0,2,5) returns a 2
=IF(OR(A1>10, A3>A1,A2>=2*A3),1,0) returns a 1
=IF(AND(A1>=10, A3>2*A1,A2>2*A3),1,NA()) returns #N/A
This function is extremely useful for creating conditional links between random variables so that a model remains internally consistent no matter what values are being generated from the input distributions.
INDEX
INDEX(array,r,c) returns the value in the rth row and the cth column of the specified array. Very useful for picking up values from tables of data when r,c or both are random variables. There is also another parameter format for INDEX.
ISNA
ISNA(ref) checks whether a value is #N/A, and returns TRUE or FALSE.
LN
LN(x) returns the natural log of x, so LN(EXP(x)) = x
LOG
LOG(x, base) returns the logarithm of x to the specified base. The base is taken as 10 if the optional parameter base is omitted, so aLOG(x,a) = x.
LOG10
LOG10(x) returns the logarithm of x to base 10, so 10LOG10(x) = x
OFFSET
OFFSET(reference, r,c,w,h) returns the value r rows below and c columns to the right of reference. If the optional parameters w and h are used, it becomes an array formula and returns an array staring at the same cell, but extending w cells wide and h cells high. For example:

OR
OR(condition1, condition2,&) returns a TRUE if any of the conditions are met, and a false otherwise. For example:
A1: 10
A2: 12
A3: 6
=OR(A1>10, A3>A1,A2>=2*A3) returns a TRUE
=OR(A1>10, A3>A1,A2<2*A3) returns a FALSE
PI
PI( ) returns the number 3.14159265358979, the mathematical constant pi, accurate to 15 digits.
ROUND
ROUND(x,digits) rounds off x to a certain number of decimal places:
ROUND(1234.5678,2) = 1234.57
ROUND(1234.5678,0) = 1235
ROUND(1234.5678,-2) = 1200
ROUNDUP
ROUNDUP(x,digits) rounds a number up, away from 0 (zero).
SIN
SIN(x) returns the sine of the given angle.
SQRT
SQRT(x) returns the square root of x, e.g. SQRT(16) = 4.
SUM
SUM({x}) returns the sum of the cells in the array {x}
SUMPRODUCT
SUMPRODUCT({x},{y},{z}, ...) multiplies corresponding components in the given arrays, and returns the sum of those products.
TODAY
TODAY( ) returns the serial number of the current date. The serial number is the date-time code used by Microsoft Excel for date and time calculations. If the cell format was General before the function was entered, the result is formatted as a date.
TRUE
TRUE( ) returns the logical value TRUE.
VLOOKUP
VLOOKUP(v,A,i) looks up in a table delineated by the area A. It searches for the value v in the first column, and then returns the value in the ith column of the same row. For example:

This is a useful function in combination with a probability distribution for selecting random or conditional values from tables. However, it can be somewhat tricky in predicting what it will do at the end of tables, and wont work properly unless the first column is put in ascending order. For these reasons we tend to use the functions OFFSET and INDEX for this purpose.
YEAR
YEAR(serial_number) returns the year corresponding to a date. The year is returned as an integer in the range 1900-9999.