Chapter8 - Random-Variate Generation 2 Purpose &...

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Unformatted text preview: Random-Variate Generation 2 Purpose & Overview Develop understanding of generating samples from a specified distribution as input to a simulation model. Illustrate some widely-used techniques for generating random variates. Inverse-transform technique Convolution technique Acceptance-rejection technique A special technique for normal distribution 3 Inverse-transform Technique The concept: For cdf function: r = F(x) Generate R sample from uniform (0,1) Find X sample: X = F-1 ( R ) r 1 x 1 r = F(x) 1 Pr( ) Pr( ( ) ) Pr( ( )) ( ) X x F R x R F x F x- ≤ = ≤ = ≤ = 4 Exponential Distribution [Inverse-transform] Exponential Distribution: Exponential cdf: To generate X 1 , X 2 , X 3 ,… generate R 1 , R 2 , R 3 ,… r = F(x) = 1 – e- λ x for x ≥ X i = F-1 (R i ) = -(1/ λ29 ln(1-R i ) Figure: Inverse-transform technique for e xp( λ = 1) 5 Example: Generate 200 variates X i with distribution exp ( λ = 1) Matlab Code for i=1:200, expnum(i)=-log(rand(1)); end Exponential Distribution [Inverse-transform] R and (1 – R ) have U(0,1) distribution 6 Uniform Distribution: Uniform cdf: To generate X 1 , X 2 , X 3 ,…, generate R 1 , R 2 , R 3 ,… Uniform Distribution [Inverse-transform] ( ) 1 x a x a r F x a x b b a b x ≤ - = = < ≤ - < ( ) i i X a b a R = +- 7 Example: Generate 500 variates X i with distribution Uniform (3,8) Matlab Code for i=1:500, uninum(i)=3+5*rand(1); end Uniform Distribution [Inverse-transform] 8...
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This note was uploaded on 03/01/2012 for the course ECON 102 taught by Professor Mehmet during the Spring '12 term at Abraham Baldwin Agricultural College.

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Chapter8 - Random-Variate Generation 2 Purpose &...

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