Page 84 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling Sandeep Kumar, Lovely Professional University

Notes Unit 6: Discrete System Simulation (III)

CONTENTS
Objectives
Introduction
6.1 Generation of Non-uniformly Distributed Random Numbers

6.2 Monte Carlo Computation vs Stochastic Simulation
6.3 Summary
6.4 Keywords
6.5 Self Assessment
6.6 Review Questions
6.7 Further Readings

Objectives

After studying this unit, you will be able to:

 Understand generation of non-uniformly distributed random number
 Describe Monte Carlo Computation vs stochastic Simulation

Introduction

Even though the RAND function can be useful for generating Uniform random numbers, most
of the time you will need to model various non-uniform distributions, such as the Normal,
Lognormal, Exponential, Gamma, and others. Monte Carlo simulation is a computerized
mathematical technique that allows people to account for risk in quantitative analysis and
decision making.

6.1 Generation of Non-uniformly Distributed Random Numbers

Principles

The uniform distribution is hardly ever used straightforwardly in any econometric model.
Other distributions, especially the normal or Gaussian distribution, are much more established.
Various methods survive to convert a uniform RNG into a non-uniform counterpart.
When it is practicable, the most suitable method to derive random number generators for a non-
uniform distribution is the inversion principle. This develops from the property:


Pr(U  u) P(u) u for U ~ U(0,1) and u [0,1].
i i
As a result, P(u) and u can be interchanged in any source. Let F(·) indicate the cumulative F (u )
–1
i
implies that u = F(e ) and therefore:
i i




Pr(e  u) Pr(F(e ) F(u)) Pr(U  F(u)) P(F(u)) F(u). as necessary.

i i i
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