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Dataplot: Random Numbers
Introduction The generation of random numbers in Dataplot is performed via subcommands under the LET command. For example,
    LET X = UNIFORM RANDOM NUMBERS FOR I = 1 1 25
    LET Y = NORMAL RUNDOM NUMBERS FOR I = 1 1 100

    LET GAMMA = 2.5
    LET Z = WEIBULL RUNDOM NUMBERS FOR I = 1 1 100

Specify Any Needed Shape Parameters The output from the random number generation is always a variable (never a parameter or function). Random numbers can be generated from a variety of distributions. Some distributions represent a family of distributions. In this case, one or more shape parameters need to be specified (via the LET command) before generating the random numbers.
SEED Command The SEED command is used to specify the seed for the random number generator.
Different Uniform Generators Available Random number generators for non-uniform distributions are ultimately built on a uniform random number generator. Dataplot now supports a number of alternatives for the uniform random number generator. See the SET RANDOM NUMBER GENERATOR for details.
Location and Scale Parameters Random numbers are generated for the standard form of a distribution. If random numbers have been generated in the variable Y for the standard form of a distribution with location parameter M and scale parameter S, the random numbers for the general form of the distribution can be generated with the following command
    LET Y2 = M + S*Y
Note that the location and scale parameters do not neccessarily correspond to the mean and standard deviation (they do for the normal distribution, but not in general).

Available Random Number Generators
Distributions Requiring No Shape Parameters The following table list the distributions for which no shape parameter is required.

Distributions With No Shape Parameters
LET Y = NORMAL RANDOM NUMBERS FOR ... generate standard normal (N(0,1)) random numbers
LET Y = UNIFORM RANDOM NUMBERS FOR ... generate uniform random numbers in the interval (0,1)
LET Y = LOGISTIC RANDOM NUMBERS FOR ... generate logistic random numbers
LET Y = DOUBLE EXPONENTIAL RANDOM NUMBERS FOR ... generate double exponential random numbers
LET Y = CAUCHY RANDOM NUMBERS FOR ... generate Cauchy random numbers
LET Y = SEMI-CIRCULAR RANDOM NUMBERS FOR ... generate semi-circular random numbers
LET Y = TRIANGULAR RANDOM NUMBERS FOR ... generate triangular random numbers
LET Y = LOGNORMAL RANDOM NUMBERS FOR ... generate lognormal random numbers
LET Y = HALFNORMAL RANDOM NUMBERS FOR ... generate halfnormal random numbers
LET Y = EXPONENTIAL RANDOM NUMBERS FOR ... generate exponential random numbers
LET Y = EXTREME VALUE TYPE 1 RANDOM NUMBERS FOR ... generate extreme value type 1 random numbers
LET Y = GUMBEL RANDOM NUMBERS FOR ... generate extreme value type 1 random numbers
LET Y = HALF CAUCHY RANDOM NUMBERS FOR ... generate half-Cauchy random numbers
LET Y = COSINE RANDOM NUMBERS FOR ... generate cosine random numbers
LET Y = ANGLIT RANDOM NUMBERS FOR ... generate anglit random numbers
LET Y = ARCSIN RANDOM NUMBERS FOR ... generate arcsin random numbers
LET Y = HYPERBOLIC SECANT RANDOM NUMBERS FOR ... generate hyperbolic secant random numbers
LET Y = HALF-LOGISTIC RANDOM NUMBERS FOR ... generate half-logistic random numbers

[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter N The following table lists the distributions requiring the shape parameter N. To specify this shape parameter, enter the following command before generating the random numbers.
    LET N = <value>
Distributions Requiring the Shape Parameter N
LET Y = DISCRETE UNIFORM RANDOM NUMBERS FOR ... generate discrete uniform random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter NU The following table lists the distributions requiring the shape parameter NU. To specify this shape parameter, enter the following command before generating the random numbers.
    LET NU = <value>
Distributions Requiring the Shape Parameter NU
LET Y = T RANDOM NUMBERS FOR ... generate t random numbers
LET Y = CHI-SQUARE RANDOM NUMBERS FOR ... generate chi-squared random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter LAMBDA The following table lists the distributions requiring the shape parameter LAMBDA. To specify this shape parameter, enter the following command before generating the random numbers.
    LET LAMBDA = <value>
Distributions Requiring the Shape Parameter LAMBDA
LET Y = TUKEY LAMBDA RANDOM NUMBERS FOR ... generate Tukey lambda random numbers
LET Y = POISSON RANDOM NUMBERS FOR ... generate Poisson random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters NU1 and NU2 The following table lists the distributions requiring the shape parameters NU1 and NU2. To specify these shape parameter, ese the following commands before generating the random numbers.
    LET NU1 = <value>
    LET NU2 = <value>
Distributions Requiring the Shape Parameters NU1 and NU2
LET Y = F RANDOM NUMBERS FOR ... generate F random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters and ALPHA and BETA The following table lists the distributions requiring the shape parameters ALPHA and BETA. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET ALPHA = <value>
    LET BETA = <value>
Distributions Requiring the Shape Parameters ALPHA amd BETA
LET Y = BETA RANDOM NUMBERS FOR ... generate beta random numbers
LET Y = POWER LAW RANDOM NUMBERS FOR ... generate power law random numbers
LET Y = ALPHA RANDOM NUMBERS FOR ... generate alpha random numbers
LET Y = POWER EXPONENTIAL RANDOM NUMBERS FOR ... generate power exponential random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter GAMMA The following table lists the distributions requiring the shape parameter GAMMA. To specify this shape parameter, enter the following command before generating the random numbers.
    LET GAMMA = <value>
Distributions Requiring the Shape Parameter GAMMA
LET Y = GAMMA RANDOM NUMBERS FOR ... generate gamma random numbers
LET Y = WEIBULL RANDOM NUMBERS FOR ... generate Weibull random numbers
LET Y = FRECHET RANDOM NUMBERS FOR ... generate extreme value type 2 random numbers
LET Y = EXTREME VALUE TYPE 2 RANDOM NUMBERS FOR ... generate extreme value type 2 random numbers
LET Y = PARETO RANDOM NUMBERS FOR ... generate Pareto random numbers
LET Y = INVERSE GAUSSIAN RANDOM NUMBERS FOR ... generate inverse gaussian random numbers
LET Y = RECIPROCAL INVERSE GAUSSIAN RANDOM NUMBERS FOR ... generate reverse inverse gaussian random numbers
LET Y = FATIGUE LIFE RANDOM NUMBERS FOR ... generate fatigue life random numbers
LET Y = WALD RANDOM NUMBERS FOR ... generate Wald random numbers
LET Y = DOUBLE GAMMA RANDOM NUMBERS FOR ... generate double gamma random numbers
LET Y = INVERTED GAMMA RANDOM NUMBERS FOR ... generate inverted gamma random numbers
LET Y = LOG GAMMA RANDOM NUMBERS FOR ... generate log gamma random numbers
LET Y = DOUBLE WEIBULL RANDOM NUMBERS FOR ... generate double Weibull random numbers
LET Y = GENERALIZED EXTREME VALUE RANDOM NUMBERS FOR ... generate generalized extreme value random numbers
LET Y = INVERTED WEIBULL RANDOM NUMBERS FOR ... generate inverted Weibull random numbers
LET Y = GENERALIZED PARETO RANDOM NUMBERS FOR ... generate generalized Pareto random numbers
LET Y = GEOMETRIC EXTREME EXPONENTIAL RANDOM NUMBERS FOR ... generate geometric extreme exponential random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter C The following table lists the distributions requiring the shape parameter C. To specify this shape parameter, enter the following command before generating the random numbers.
    LET C = <value>
Distributions Requiring the Shape Parameter C
LET Y = POWER FOR ... generate power random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters MU and SD The following table lists the distributions requiring the shape parameters MU and SD. To specify these shape parameter, enter the following commands before generating the random numbers.
    LET MU = <value>
    LET SD = <value>
Distributions Requiring the Shape Parameters MU and SD
LET Y = FOLDED NORMAL FOR ... generate folded normal random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters MU1, SD1, MU2, SD2, and P The following table lists the distributions requiring the shape parameters MU1, SD1, MU2, SD2, and P. To specify these shape parameter, enter the following commands before generating the random numbers.
    LET MU1 = <value>
    LET SD1 = <value>
    LET MU2 = <value>
    LET SD2 = <value>
    LET P = <value>
Distributions Requiring the Shape Parameters MU1, SD1, MU2, SD2, and P
LET Y = NORMAL MIXTURE FOR ... generate normal mixture random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters NU and LAMBDA The following table lists the distributions requiring the shape parameters NU and LAMBDA. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET NU = <value>
    LET LAMBDA = <value>
Distributions Requiring the Shape Parameters NU and LAMBDA
LET Y = NON-CENTRAL CHI-SQUARE FOR ... generate non-central chi-square random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters NU1, NU2, and LAMBDA The following table lists the distributions requiring the shape parameters NU1, NU2, and LAMBDA. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET NU1 = <value>
    LET NU2 = <value>
    LET LAMBDA = <value>
Distributions Requiring the Shape Parameters NU1, NU2, and LAMBDA
LET Y = NON-CENTRAL F FOR ... generate non-central F random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters NU1, NU2, LAMBDA1, and LAMBDA2 The following table lists the distributions requiring the shape parameters NU1, NU2, LAMBDA1, and LAMBDA2. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET NU1 = <value>
    LET NU2 = <value>
    LET LAMBDA1 = <value>
    LET LAMBDA2 = <value>
Distributions Requiring the Shape Parameters NU1, NU2, LAMBDA1, and LAMBDA2
LET Y = DOUBLY NON-CENTRAL F FOR ... generate doubly non-central F random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter P The following table lists the distributions requiring the shape parameter P. To specify this shape parameter, enter the following command before generating the random numbers.
    LET P = <value>
Distributions Requiring the Shape Parameter P
LET Y = GEOMETRIC RANDOM NUMBERS FOR ... generate geometric random numbers
LET Y = POWER NORMAL RANDOM NUMBERS FOR ... generate power normal random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters P and N The following table lists the distributions requiring the shape parameters P and N. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET P = <value>
    LET N = <value>
Distributions Requiring the Shape Parameters P and N
LET Y = BINOMIAL RANDOM NUMBERS FOR ... generate binomial random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters P and K The following table lists the distributions requiring the shape parameters P and K. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET P = <value>
    LET K = <value>
Distributions Requiring the Shape Parameters P and K
LET Y = NEGATIVE BINOMIAL RANDOM NUMBERS FOR ... generate negative binomial random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters L, K, N, and M The following table lists the distributions requiring the shape parameters L, K, N, and M. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET L = <value>
    LET K = <value>
    LET N = <value>
    LET M = <value>
Distributions Requiring the Shape Parameters L, K, N, and M
LET Y = NEGATIVE BINOMIAL RANDOM NUMBERS FOR ... generate negative binomial random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter DELTA The following table lists the distributions requiring the shape parameter DELTA. To specify this shape parameter, enter the following command before generating the random numbers.
    LET DELTA = <value>
Distributions Requiring the Shape Parameter DELTA
LET Y = LOG-LOGISTIC RANDOM NUMBERS FOR ... generate log-logistic random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter ALPHA The following table lists the distributions requiring the shape parameter ALPHA. To specify this shape parameter, enter the following command before generating the random numbers.
    LET ALPHA = <value>
Distributions Requiring the Shape Parameter ALPHA
LET Y = LOG DOUBLE EXPONENTIAL RANDOM NUMBERS FOR ... generate log double exponential random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter BETA The following table lists the distributions requiring the shape parameter BETA. To specify this shape parameter, enter the following command before generating the random numbers.
    LET BETA = <value>
Distributions Requiring the Shape Parameter BETA
LET Y = BRADFORD RANDOM NUMBERS FOR ... generate Bradford random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter B The following table lists the distributions requiring the shape parameter B. To specify this shape parameter, enter the following command before generating the random numbers.
    LET B = <value>
Distributions Requiring the Shape Parameter B
LET Y = RECIPROCAL RANDOM NUMBERS FOR ... generate reciprocal random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters C and B The following table lists the distributions requiring the shape parameters C and B. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET C = <value>
    LET B = <value>
Distributions Requiring the Shape Parameters C and B
LET Y = GOMPERTZ RANDOM NUMBERS FOR ... generate Gompertz random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameter THETA The following table lists the distributions requiring the shape parameter THETA. To specify this shape parameter, enter the following command before generating the random numbers.
    LET THETA = <value>
Distributions Requiring the Shape Parameter THETA
LET Y = LOGARITHMIC SERIES RANDOM NUMBERS FOR ... generate logarithmic series random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters GAMMA and THETA The following table lists the distributions requiring the shape parameters THETA and GAMMA. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET THETA = <value>
    LET GAMMA = <value>
Distributions Requiring the Shape Parameters THETA and GAMMA
LET Y = EXPONENTIATED WEIBULL RANDOM NUMBERS FOR ... generate exponentiated Weibull random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters N and THETA The following table lists the distributions requiring the shape parameters THETA and N. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET THETA = <value>
    LET N = <value>
Distributions Requiring the Shape Parameters THETA and N
LET Y = TWO-SIDED POWER RANDOM NUMBERS FOR ... generate two-sided power random numbers
[ Dataplot  / Dataplot Random Numbers ]
Distributions Requiring the Shape Parameters SCALE1, GAMMA1, LOC2, SCALE2, and GAMMA2 The following table lists the distributions requiring the shape parameters SCALE1, GAMMA1, LOC2, SCALE2, and GAMMA2. To specify these shape parameters, enter the following commands before generating the random numbers.
    LET SCALE1 = <value>
    LET GAMMA1 = <value>
    LET LOC2 = <value>
    LET SCALE2 = <value>
    LET GAMMA2 = <value>
Distributions Requiring the Shape Parameters SCALE1, GAMMA1, LOC2, SCALE2, and GAMMA2
LET Y = BIWEIBULL RANDOM NUMBERS FOR ... generate bi-Weibull random numbers
[ Dataplot  / Dataplot Random Numbers ]
Random Numbers for Multivariate Distributions In addition to the above univariate distributions, Dataplot can generate random numbers for multinomial and multivariate normal random numbers. These multivariate distributions return a matrix, rather than a vector, of random numbers.

To generate multivariate normal random numbers, enter the following commands:

    LET MU = DATA <list of p means>
    READ MATRIX SIGMA
    <pxp set of values>
    END OF DATA
    LET N = <value>
    LET M = MULTIVARIATE NORMAL RANDOM NUMBERS MU SIGMA N
Note that M will be an NxP matrix. N is the number of rows generated for each component and their are P components to the multivariate normal. SIGMA is the pxp variance-covariance matrix of the multivariate normal. SIGMA will be checked to ensure that it is a positive definite matrix. MU is a vector specifying the means of the p components.

To generate multinomial random numbers, enter

    LET P = DATA <list of probabilities that sum to 1>
    LET NEVENTS = <value>
    LET NCAT = SIZE P
    LET N = <value>
    LET M = MULTINOMIAL RANDOM NUMBERS P NEVENTS NCAT N
[ Dataplot  / Dataplot Random Numbers ]

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Date created: 06/05/2001
Last updated: 09/20/2016
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