Random Numbers

This function is Excel compatible.

RANDBETWEEN.

p: probability of success

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

RAND, RANDBETWEEN.

a: parameter of the Beta distribution

b: parameter of the Beta distribution

RAND, RANDGAMMA.

bottom: lower limit

top: upper limit

If bottom > top, RANDBETWEEN returns #NUM!

This function is Excel compatible.

RAND, RANDUNIFORM.

p: probability of success in a single trial

n: number of trials

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

RAND, RANDBETWEEN.

a: scale parameter of the distribution

If a < 0 RANDCAUCHY returns #NUM!

RAND.

df: degrees of freedom

RAND, RANDGAMMA.

val_range: possible values of the random variable

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

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

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!

RANDBETWEEN, RAND.

b: parameter of the exponential distribution

RAND, RANDBETWEEN.

a: scale parameter of the exponential power distribution

b: exponent of the exponential power distribution

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.

df1: numerator degrees of freedom

df2: denominator degrees of freedom

RAND, RANDGAMMA.

a: shape parameter of the Gamma distribution

b: scale parameter of the Gamma distribution

If a ≤ 0, RANDGAMMA returns #NUM!

RAND.

p: probability of success in a single trial

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

RAND.

a: parameter of the Gumbel distribution

b: parameter of the Gumbel distribution

type: type of the Gumbel distribution, defaults to 1

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

RAND.

n1: number of objects of type 1

n2: number of objects of type 2

t: total number of objects selected

RAND.

RAND.

a: parameter of the Laplace distribution

RAND.

c: parameter of the Lévy distribution

α: parameter of the Lévy distribution

β: parameter of the Lévy distribution, defaults to 0

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.

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

RAND.

p: probability

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

RAND.

a: parameter of the logistic distribution

RAND.

ζ: parameter of the lognormal distribution

σ: standard deviation of the distribution

If σ < 0, RANDLOGNORM returns #NUM!

RAND.

p: probability of success in a single trial

n: number of failures

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

RAND, RANDBETWEEN.

μ: mean of the distribution

σ: standard deviation of the distribution

If σ < 0, RANDNORM returns #NUM!

RAND.

a: lower limit of the tail

σ: standard deviation of the normal distribution

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.

a: parameter of the Pareto distribution

b: parameter of the Pareto distribution

RAND.

λ: parameter of the Poisson distribution

If λ < 0 RANDPOISSON returns #NUM!

RAND, RANDBETWEEN.

σ: scale parameter of the Rayleigh distribution

RAND.

a: lower limit of the tail

σ: scale parameter of the Rayleigh distribution

RAND, RANDRAYLEIGH.

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

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.

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!

RANDNORM, RANDSTDIST.

df: degrees of freedom

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

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, RANDSNORM.

df: degrees of freedom

RAND.

a: lower limit of the uniform distribution

b: upper limit of the uniform distribution

If a > b RANDUNIFORM returns #NUM!

RANDBETWEEN, RAND.

a: scale parameter of the Weibull distribution

b: shape parameter of the Weibull distribution

RAND.

d1: first value

d2: second value

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.