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Generating RVs

Generating RVs - 42 ChapterZ Static Simulations TABLE 2.4...

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Unformatted text preview: 42 ChapterZ Static Simulations TABLE 2.4 Summary of methods for generating random variates from common distributions Distribution: Parameters Formuia Bernoulli p , _ {I if U =E p ‘ 0nu>p l _ Uniform a < b X: a + {be a) U Triangular X: V2 (U, + U2) . . i — Symmetric triangular X = a + (i 5—) (Ul + U2) Right triangular ‘ X = a + (c — an]? Approximately normal X :- U] + U2 4— . . . + Um - 6 Approximately normat X = p. + 0' (U, + U2 + . . .+ {1,2 e 6) Exponential X: up ln(U) 1' its-1,1- 1 Discrete uniform k. k + l, . . . . k + m X z k + int{(m + DU] «lift/Sp] 01,112,...,am E "i pnpz.....p,. 't‘ + <U< + + mprrica al<a2<...<am “23.01 P2 \P1 P; P: pl+p2+...+pm=l azif‘n.<U=_<.pl+p2 amifU>p1+p2+...+pwl random variates from other distributions, both continuous and discrete. Here we present useful techniques for generating random variates from a few relatively simple distributions. We will then use these techniques in this and subsequent chap- ters. Other texts present the theory behind these techniques. See, for example, Banks (1998). Chapter 5; Banks et a1. (2001), Chapter 8; Law and Kelton (2000), Chapter 8; Pidd (1992), Chapter 12, sections 5—7; and Fisitman (1996), Chapter 3. All of these random variate generation techniques, which are summarized in Table 2.4, as- sume that you have a procedure or function that wiii generate a sequence of iride- pendent uniformly distributed random variates between 0 and 1. Such a function—— called RANDO in Excel—is availabie in virtually all spreadsheet programs. We will assume that U represents a uniformly distributed random variate between 0 and 1; that is, U = RANDO in Excel. Bernoulli Random Variates A Bernoulli random variable, X, which has the value 1 with probability p and the value 0 with probability 1 — p, can be used to randomiy select between twu alterna- tives. If X = 1, then alternative 1 is selected; otherwise (X = 0), alternative 2 is se« ...
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