Chapter 2 Generating Random Digits and Uniform Random Numbers over (0,1)

• 2.3 Multiplicative Congruential Random Number Generators LCGIs.txt LCGs.txt LCG.txt

• 2.3.1 Linear Congruential Random Number Generators
  • Table2_1.txt
• 2.3.2 Multiplicative Congruential Random Number Generators
  • 2.3.2.1 RANDU
    • RANDU.txt
  • 2.3.2.2 GGL
    • GGL.txt
  • 2.3.2.3 Comparing RANDU and GGL
    • Table2_2.txt Table2_3.txt
  • 2.3.2.4 A Deficiency of Multiplicative Congruential Generators
    • Fig2_1.txt

• 2.4 Shuffling

• Bays-Durham shuffling
  • LCGIs_BD.txt LCG_BD.txt Fig2223.txt

• 2.5 Fibonacci Random Number Generators

• 2.5.1 Lagged Fibonacci Random Number Generator
  • LFG.txt
  • Knuth.txt
• 2.5.2 Add-with-carry Random Number Generator
  • AWCG.txt
• 2.5.2' Subtract-with-borrow Random Number Generator
  • SWBG.txt
• 2.5.3 Multiple Recursive Random Number Generator
  • MRG.txt

• 2.7

• 2.8 Exercises

• RANEXCEL.txt ex2_2.txt ex2_3.txt ex2_4.txt
• ex2_7.txt RANVB.txt ex2_8.txt

Chapter 3 The Inversion Method of Generating Random Numbers from Continuous and Discrete Distributions

• 3.1 The Inversion Method for Continuous Distributions

• 3.1.1 The Exponential Distribution
  • ranexpon.txt
• 3.1.2 The Beta Distribution, B(alpha,1)
  • ranbetaa1.txt
• 3.1.3 The Beta Distribution, B(1,beta)
  • ranbeta1b.txt
• 3.1.4 The Logistic Distribution
  • ranlogist.txt
• 3.1.5 The Cauchy Distribution
  • rancauchy.txt
• 3.1.6 The Pareto Distribution
  • ranpareto.txt
• 3.1.7 The Weibull Distribution
  • ranweibull.txt

• 3.2 The Table Look-up Method for Discrete Distributions

• 3.2.1 Examples of the Table Look-up Method
  • 3.2.1.1 The Discrete Uniform Distribution
    • randuni.txt
  • 3.2.1.2 The Bernoulli Distribution, Bin(1,p)
    • ranbern.txt
• 3.2.3 The Binomial Distribution, Bin(n,p)
  • 3.2.3.1 Table Look-up for the Binomial Distribution
    • ranbino.txt
  • 3.2.3.2 Modified Table Look-up for the Binomial Distribution
    • ranbinor.txt
  • 3.2.3.3 Normal Approximation to the Binomial Distribution
    • ranbinoap.txt
• 3.2.4 The Geometric Distribution (the discrete exponential)
  • 3.2.4.1 Discretized Exponential Approach
    • rangeodea.txt rangeoi.txt
  • 3.2.4.2 Modified Table Look-up Approach (with recursion)
    • rangeor.txt
  • 3.2.4.3 Tossing a Biased Coin Approach
    • rangeot.txt
• 3.2.5 The Negative Binomial Distribution
  • 3.2.5.1 Modified Table Look-up Approach (with recursion)
    • rannbr.txt
  • 3.2.5.2 Tossing a Biased Coin Approach
    • rannbt.txt
• 3.2.6 The Hypergeometric Distribution
  • ranhygeor.txt ranhygeor1.txt

• 3.2.7 The Poisson Distribution
  • 3.2.7.1 Modified Table Look-up
    • ranpr.txt
  • 3.2.7.2 Normal Approximation Approach
    • ranpap.txt
  • 3.2.7.3 Exponential Interarrival Time Approach
    • ranpeit.txt

• 3.3 Exercises

Chapter 4 Other Methods for Generating Random Numbers from Continuous and Discrete Distributions

• 4.1 The Acceptance-Rejection Method(the continuous case)

• ex4_1_1.txt ex4_1_2.txt ex4_1_3.txt

• 4.1.1 The Polar Method for Generating
  • rannpolar.txt
• 4.1.2 The Squeeze Method
  • 　

• 4.2 The Convolution Method

• rantri.txt ex4_6.txt ranbinoc.txt rangamc.txt ranchisqc.txt

• 4.3 Ratio of Uniform Distribution Method

• rancauchyru.txt ranexponru.txt

• 4.4 The Composition Method

• ex4_13.txt ex4_17.txt

• 4.5 The Multivariate Normal Distribution

• 4.8 Exercises

Chapter 5 Integral Estimation - Variance Reduction Techniques

• Thomas N. Herzog and Graham Lord "Applications of Monte Carlo Methods to Finance and Insurance", ACTEX Pub. 2002 ISBN:1-56698-433-5.

• Its Solutions Manual(Thin Booklet) ISBN:1-56698-443-2.

• Official Errata: http://www.actexmadriver.com/client/client_pages/actex_errata_MonteCarlo.cfm

This is a GAUSS version of its "complete" programming guide. Buy and read the textbook above along with this guide.

by Yosuke Amijima

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