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Generation of some First-Order Autoregressive Markovian Sequences of Positive Random Variables with Given Marginal Distributions

  • A. J. Lawrance
  • P. A. W. Lewis
Part of the Progress in Computer Science book series (PCS, volume 2)

Abstract

Methods for simulating dependent sequences of continuous positivevalued random variables with exponential, uniform, Gamma, and mixed exponential marginal distributions are given. In most cases the sequences are first-order, linear autoregressive, Markovian processes. A very broad two-parameter family of this type, GNEAR(l), with exponential marginals and both positive and negative correlation is defined and its transformation to a similar multiplicative process with uniform marginals is given. It is shown that for a subclass of this two-parameter family extension to mixed exponential marginals is possible, giving a model of broad applicability for analyzing data and modelling stochastic systems, although negative correlation is more difficult to obtain than in the exponential case. Finally, two schemes for autoregressive sequences with Gamma distributed marginals are outlined. Efficient simulation of some of these schemes is discussed.

Keywords

Sample Path Dependent Sequence Exponential Random Variable Uniform Random Number Positive Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1982

Authors and Affiliations

  • A. J. Lawrance
    • 1
  • P. A. W. Lewis
    • 2
  1. 1.Dept. StatisticsUniversity of BirminghamBirminghamEngland
  2. 2.Dept. Operations ResearchNaval Postgraduate SchoolMontereyUSA

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