# Random Numbers

• RAND a random number between zero and one
• RANDBERNOULLI random variate from a Bernoulli distribution
• RANDBETA random variate from a Beta distribution
• RANDBETWEEN a random integer number between and including bottom and top
• RANDBINOM random variate from a binomial distribution
• RANDCAUCHY random variate from a Cauchy or Lorentz distribution
• RANDCHISQ random variate from a Chi-square distribution
• RANDDISCRETE random variate from a finite discrete distribution
• RANDEXP random variate from an exponential distribution
• RANDEXPPOW random variate from an exponential power distribution
• RANDFDIST random variate from an F distribution
• RANDGAMMA random variate from a Gamma distribution
• RANDGEOM random variate from a geometric distribution
• RANDGUMBEL random variate from a Gumbel distribution
• RANDHYPERG random variate from a hypergeometric distribution
• RANDLANDAU random variate from the Landau distribution
• RANDLAPLACE random variate from a Laplace distribution
• RANDLEVY random variate from a Lévy distribution
• RANDLOG random variate from a logarithmic distribution
• RANDLOGISTIC random variate from a logistic distribution
• RANDLOGNORM random variate from a lognormal distribution
• RANDNEGBINOM random variate from a negative binomial distribution
• RANDNORM random variate from a normal distribution
• RANDNORMTAIL random variate from the upper tail of a normal distribution with mean 0
• RANDPARETO random variate from a Pareto distribution
• RANDPOISSON random variate from a Poisson distribution
• RANDRAYLEIGH random variate from a Rayleigh distribution
• RANDRAYLEIGHTAIL random variate from the tail of a Rayleigh distribution
• RANDSNORM random variate from a skew-normal distribution
• RANDSTDIST random variate from a skew-t distribution
• RANDTDIST random variate from a Student t distribution
• RANDUNIFORM random variate from the uniform distribution from a to b
• RANDWEIBULL random variate from a Weibull distribution
• SIMTABLE one of the values in the given argument list depending on the round number of the simulation tool

## RAND

RAND a random number between zero and one

`RAND()`

### Microsoft Excel Compatibility

This function is Excel compatible.

## RANDBERNOULLI

RANDBERNOULLI random variate from a Bernoulli distribution

### Synopsis

`RANDBERNOULLI(p)`

### Arguments

p: probability of success

### Note

If p < 0 or p > 1 RANDBERNOULLI returns #NUM!

## RANDBETA

RANDBETA random variate from a Beta distribution

### Synopsis

`RANDBETA(a,b)`

### Arguments

a: parameter of the Beta distribution

b: parameter of the Beta distribution

## RANDBETWEEN

RANDBETWEEN a random integer number between and including bottom and top

### Synopsis

`RANDBETWEEN(bottom,top)`

### Arguments

bottom: lower limit

top: upper limit

### Note

If bottom > top, RANDBETWEEN returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## RANDBINOM

RANDBINOM random variate from a binomial distribution

### Synopsis

`RANDBINOM(p,n)`

### Arguments

p: probability of success in a single trial

n: number of trials

### Note

If p < 0 or p > 1 RANDBINOM returns #NUM! If n < 0 RANDBINOM returns #NUM!

## RANDCAUCHY

RANDCAUCHY random variate from a Cauchy or Lorentz distribution

### Synopsis

`RANDCAUCHY(a)`

### Arguments

a: scale parameter of the distribution

### Note

If a < 0 RANDCAUCHY returns #NUM!

RAND.

## RANDCHISQ

RANDCHISQ random variate from a Chi-square distribution

### Synopsis

`RANDCHISQ(df)`

### Arguments

df: degrees of freedom

## RANDDISCRETE

RANDDISCRETE random variate from a finite discrete distribution

### Synopsis

`RANDDISCRETE(val_range,prob_range)`

### Arguments

val_range: possible values of the random variable

prob_range: probabilities of the corresponding values in val_range, defaults to equal probabilities

### Description

RANDDISCRETE returns one of the values in the val_range. The probabilities for each value are given in the prob_range.

### Note

If the sum of all values in prob_range is not one, RANDDISCRETE returns #NUM! If val_range and prob_range are not the same size, RANDDISCRETE returns #NUM! If val_range or prob_range is not a range, RANDDISCRETE returns #VALUE!

## RANDEXP

RANDEXP random variate from an exponential distribution

### Synopsis

`RANDEXP(b)`

### Arguments

b: parameter of the exponential distribution

## RANDEXPPOW

RANDEXPPOW random variate from an exponential power distribution

### Synopsis

`RANDEXPPOW(a,b)`

### Arguments

a: scale parameter of the exponential power distribution

b: exponent of the exponential power distribution

### Description

For b = 1 the exponential power distribution reduces to the Laplace distribution.

For b = 2 the exponential power distribution reduces to the normal distribution with σ = a/sqrt(2)

RAND.

## RANDFDIST

RANDFDIST random variate from an F distribution

### Synopsis

`RANDFDIST(df1,df2)`

### Arguments

df1: numerator degrees of freedom

df2: denominator degrees of freedom

## RANDGAMMA

RANDGAMMA random variate from a Gamma distribution

### Synopsis

`RANDGAMMA(a,b)`

### Arguments

a: shape parameter of the Gamma distribution

b: scale parameter of the Gamma distribution

### Note

If a ≤ 0, RANDGAMMA returns #NUM!

RAND.

## RANDGEOM

RANDGEOM random variate from a geometric distribution

### Synopsis

`RANDGEOM(p)`

### Arguments

p: probability of success in a single trial

### Note

If p < 0 or p > 1 RANDGEOM returns #NUM!

RAND.

## RANDGUMBEL

RANDGUMBEL random variate from a Gumbel distribution

### Synopsis

`RANDGUMBEL(a,b,type)`

### Arguments

a: parameter of the Gumbel distribution

b: parameter of the Gumbel distribution

type: type of the Gumbel distribution, defaults to 1

### Note

If type is neither 1 nor 2, RANDGUMBEL returns #NUM!

RAND.

## RANDHYPERG

RANDHYPERG random variate from a hypergeometric distribution

### Synopsis

`RANDHYPERG(n1,n2,t)`

### Arguments

n1: number of objects of type 1

n2: number of objects of type 2

t: total number of objects selected

RAND.

## RANDLANDAU

RANDLANDAU random variate from the Landau distribution

### Synopsis

`RANDLANDAU()`

RAND.

## RANDLAPLACE

RANDLAPLACE random variate from a Laplace distribution

### Synopsis

`RANDLAPLACE(a)`

### Arguments

a: parameter of the Laplace distribution

RAND.

## RANDLEVY

RANDLEVY random variate from a Lévy distribution

### Synopsis

`RANDLEVY(c,α,β)`

### Arguments

c: parameter of the Lévy distribution

α: parameter of the Lévy distribution

β: parameter of the Lévy distribution, defaults to 0

### Description

For α = 1, β=0, the Lévy distribution reduces to the Cauchy (or Lorentzian) distribution.

For α = 2, β=0, the Lévy distribution reduces to the normal distribution.

### Note

If α ≤ 0 or α > 2, RANDLEVY returns #NUM! If β < -1 or β > 1, RANDLEVY returns #NUM!

RAND.

## RANDLOG

RANDLOG random variate from a logarithmic distribution

### Synopsis

`RANDLOG(p)`

p: probability

### Note

If p < 0 or p > 1 RANDLOG returns #NUM!

RAND.

## RANDLOGISTIC

RANDLOGISTIC random variate from a logistic distribution

### Synopsis

`RANDLOGISTIC(a)`

### Arguments

a: parameter of the logistic distribution

RAND.

## RANDLOGNORM

RANDLOGNORM random variate from a lognormal distribution

### Synopsis

`RANDLOGNORM(ζ,σ)`

### Arguments

ζ: parameter of the lognormal distribution

σ: standard deviation of the distribution

### Note

If σ < 0, RANDLOGNORM returns #NUM!

RAND.

## RANDNEGBINOM

RANDNEGBINOM random variate from a negative binomial distribution

### Synopsis

`RANDNEGBINOM(p,n)`

### Arguments

p: probability of success in a single trial

n: number of failures

### Note

If p < 0 or p > 1 RANDNEGBINOM returns #NUM! If n < 1 RANDNEGBINOM returns #NUM!

## RANDNORM

RANDNORM random variate from a normal distribution

### Synopsis

`RANDNORM(μ,σ)`

### Arguments

μ: mean of the distribution

σ: standard deviation of the distribution

### Note

If σ < 0, RANDNORM returns #NUM!

RAND.

## RANDNORMTAIL

RANDNORMTAIL random variate from the upper tail of a normal distribution with mean 0

### Synopsis

`RANDNORMTAIL(a,σ)`

### Arguments

a: lower limit of the tail

σ: standard deviation of the normal distribution

### Note

The method is based on Marsaglia's famous rectangle-wedge-tail algorithm (Ann Math Stat 32, 894-899 (1961)), with this aspect explained in Knuth, v2, 3rd ed, p139, 586 (exercise 11).

RAND.

## RANDPARETO

RANDPARETO random variate from a Pareto distribution

### Synopsis

`RANDPARETO(a,b)`

### Arguments

a: parameter of the Pareto distribution

b: parameter of the Pareto distribution

RAND.

## RANDPOISSON

RANDPOISSON random variate from a Poisson distribution

### Synopsis

`RANDPOISSON(λ)`

### Arguments

λ: parameter of the Poisson distribution

### Note

If λ < 0 RANDPOISSON returns #NUM!

## RANDRAYLEIGH

RANDRAYLEIGH random variate from a Rayleigh distribution

### Synopsis

`RANDRAYLEIGH(σ)`

### Arguments

σ: scale parameter of the Rayleigh distribution

RAND.

## RANDRAYLEIGHTAIL

RANDRAYLEIGHTAIL random variate from the tail of a Rayleigh distribution

### Synopsis

`RANDRAYLEIGHTAIL(a,σ)`

### Arguments

a: lower limit of the tail

σ: scale parameter of the Rayleigh distribution

## RANDSNORM

RANDSNORM random variate from a skew-normal distribution

### Synopsis

`RANDSNORM(𝛼,𝜉,𝜔)`

### Arguments

𝛼: shape parameter of the skew-normal distribution, defaults to 0

𝜉: location parameter of the skew-normal distribution, defaults to 0

𝜔: scale parameter of the skew-normal distribution, defaults to 1

### Description

The random variates are drawn from a skew-normal distribution with shape parameter 𝛼. When 𝛼=0, the skewness vanishes, and we obtain the standard normal density; as 𝛼 increases (in absolute value), the skewness of the distribution increases; when 𝛼 approaches infinity the density converges to the so-called half-normal (or folded normal) density function; if the sign of 𝛼 changes, the density is reflected on the opposite side of the vertical axis.

### Note

The mean of a skew-normal distribution with location parameter 𝜉=0 is not 0. The standard deviation of a skew-normal distribution with scale parameter 𝜔=1 is not 1. The skewness of a skew-normal distribution is in general not 𝛼. If 𝜔 < 0, RANDSNORM returns #NUM!

## RANDSTDIST

RANDSTDIST random variate from a skew-t distribution

### Synopsis

`RANDSTDIST(df,𝛼)`

### Arguments

df: degrees of freedom

𝛼: shape parameter of the skew-t distribution, defaults to 0

### Note

The mean of a skew-t distribution is not 0. The standard deviation of a skew-t distribution is not 1. The skewness of a skew-t distribution is in general not 𝛼.

## RANDTDIST

RANDTDIST random variate from a Student t distribution

### Synopsis

`RANDTDIST(df)`

### Arguments

df: degrees of freedom

RAND.

## RANDUNIFORM

RANDUNIFORM random variate from the uniform distribution from a to b

### Synopsis

`RANDUNIFORM(a,b)`

### Arguments

a: lower limit of the uniform distribution

b: upper limit of the uniform distribution

### Note

If a > b RANDUNIFORM returns #NUM!

## RANDWEIBULL

RANDWEIBULL random variate from a Weibull distribution

### Synopsis

`RANDWEIBULL(a,b)`

### Arguments

a: scale parameter of the Weibull distribution

b: shape parameter of the Weibull distribution

RAND.

## SIMTABLE

SIMTABLE one of the values in the given argument list depending on the round number of the simulation tool

### Synopsis

`SIMTABLE(d1,d2,…)`

d1: first value

d2: second value

### Description

SIMTABLE returns one of the values in the given argument list depending on the round number of the simulation tool. When the simulation tool is not activated, SIMTABLE returns d1.

With the simulation tool and the SIMTABLE function you can test given decision variables. Each SIMTABLE function contains the possible values of a simulation variable. In most valid simulation models you should have the same number of values dN for all decision variables. If the simulation is run more rounds than there are values defined, SIMTABLE returns #N/A error (e.g. if A1 contains `=SIMTABLE(1)' and A2 `=SIMTABLE(1,2)', A1 yields #N/A error on the second round).

The successive use of the simulation tool also requires that you give to the tool at least one input variable having RAND() or any other RAND<distribution name>() function in it. On each round, the simulation tool iterates for the given number of rounds over all the input variables to reevaluate them. On each iteration, the values of the output variables are stored, and when the round is completed, descriptive statistical information is created according to the values.