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Generating Random Numbers

  • Generating a random number from an arbitrary probability distribution is equivalent to generating a random number from the uniform distribution [0,1], such that each value between 0 and 1 is equally likely to occur. Methods used are:
  • Inverse transform method to simulate various distributions
    • Converting a random number between 0 and 1, to its equivalent number from an arbitrary probability distribution)
    • Inverse transform method maps random numbers to standard normal distribution so that monte carlo simulation follows a normal distribution
    • Alternative methods used, where the inverse is not easy to calculate: The acceptance-rejection method, the composition method, the ratio of uniforms method etc.

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