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Appendix C Formula Functions Reference 485
Random Functions
Random Functions
You can create formulas that generate real numbers by effectively “rolling the dice” within the
constraints of the specified distribution. The random numbers are generated using the
Mersenne-Twister technique. See Matsumoto and Nishimura (1998) in the reference section of the
JMP Statistics and Graphics Guide for details. Also see the JMP Scripting Guide for details about syntax.
Random Uniform
Generates random numbers uniformly between 0 and 1. This means that any number between 0 and 1
is as likely to be generated as any other. The result is an approximately even distribution. You can shift
the distribution and change its range with constants. For example, 5 + Random Uniform()*20
generates uniform random numbers between 5 and 25.
Random Normal
Generates random numbers that approximate a normal distribution with a mean of 0 and standard
deviation of 1 if no arguments are used, or with the mean and standard deviation entered as arguments.
The normal distribution is bell shaped and symmetrical. You can also modify the Random Normal
function with constants if no arguments are entered to give a normal distribution with specific mean
and standard deviation. For example, the formula Random Normal()*5 + 30 generates a random
normal variable with a mean of 30 and a standard deviation of 5.
C Formula Functions Reference
Random Exp
Generates a single parameter exponential distribution for the distribution parameter lambda=1. You
can modify the exponential function to use a different lambda.
For example, Random Exp()/.1 generates an exponential distribution for lambda=0.1. The
exponential distribution is often used to model simple failure time data, where lambda is the failure
rate.
Random Gamma
Gives a gamma distribution for the parameter, alpha, you enter as the function argument. The gamma
distribution describes the time until the k th occurrence of an event. The gamma distribution can also
have a scale parameter, beta. A gamma variate with shape parameter alpha and scale beta can be
generated with the formula beta*Random Gamma(alpha). If 2*alpha is an integer, a Chi-squared
variate with 2*alpha degrees of freedom is generated with the formula 2*Random Gamma(alpha).
Random Beta
Generates a pseudo-random number distributed Beta(alpha, beta).
Random Cauchy
Generates a Cauchy distribution with location parameter 0 and scale parameter 1. The Cauchy
distribution is bell shaped and symmetric but has heavier tails than the normal distribution. A Cauchy
variate with location parameter alpha and scale parameter beta can be generated with the formula
alpha+beta*Random Cauchy().