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MULTINOMIAL RANDOM NUMBERName:
The multinomial distribution extends this by allowing k possible outcomes. These outcomes are mutually exclusive with each outcome having probability pi. The pi must sum to 1 and are the same for each trial. The multinomial distribution is the probability that each event occurs xi times (i = 1, 2, ..., k) in the n trials. For univariate distributions, Dataplot generates random numbers using the common syntax
LET Y = <dist> RANDOM NUMBERS FOR I = 1 1 N LET Y = LOC + SCALE*Y Multivariate distributions, however, generally require matrix operations. For this reason, random numbers for multivariate distributions each have their own unique syntax. To generate multinomial random numbers, you need to specify a variable containing the k probabilities for each outcome (these probabilities must sum to 1), a scalar value specifying the number of trials (n), and a scalar value specifying the number of multinomial events (nevents) to simulate. The output is a matrix with nevent rows and k columns. Each row of the matrix should sum to n.
where <p> is a variable containing the desired probabilities for each outcome; <n> is a number or parameter specifying the desired number of trials; <nevents> is a number or parameter specifying the number of multinomial events being generated; and where <mat> is a matrix where the resulting multinomial random numbers are stored. Dataplot determines the number of possible outcomes from the number of rows in the <p> variable. The returned matrix will have <nevents> rows and columns equal to the number of rows in <p>.
LET N = 100 LET NEVENTS = 10 LET M = MULTINOMIAL RANDOM NUMBERS P N
"Non-Uniform Random Variate Generation", Luc Devroye, Springer-Verlang, 1986, p. 559.
dimension 100 columns . let p = data 0.2 0.1 0.2 0.3 0.2 let n = 200 let nevents = 10 . let m = multinomial random numbers p n nevents . set write decimals 0 print mDataplot generated the following output. MATRIX M -- 10 ROWS -- 5 COLUMNS VARIABLES--M1 M2 M3 M4 M5 33 14 46 67 40 48 22 38 59 33 46 19 38 60 37 37 20 35 61 47 37 28 33 61 41 40 17 35 69 39 33 16 37 68 46 35 24 39 66 36 39 17 39 62 43 33 18 51 54 44
Date created: 5/21/2003 |