Abstract
I outlined the general process of simulation design in Chap. 8. One topic I did not address applies to stochastic simulations. This is the generation of random occurrences based on random numbers. Random numbers are what make simulations stochastic. In fact, “stochastic” means random. But what is a random number and how are they generated? These are the questions for this chapter.
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Notes
- 1.
See https://en.wikipedia.org/wiki/Form_follows_function. Last accessed January 14, 2023.
- 2.
See the Popular Science article by Caroline Delbert (August 18, 2021) at https://www.popularmechanics.com/science/math/a37329769/supercomputer-calculated-pi-to-record-breaking-628-trillion-digits/. Last accessed February 16, 2022.
- 3.
See https://en.wikipedia.org/wiki/Fibonacci_number. Last accessed February 21, 2022.
- 4.
See the Wikipedia article at https://en.wikipedia.org/wiki/Fibonacci_number for some comments about the staring values. Last accessed February 21, 2022.
- 5.
As of February 16, 2022.
- 6.
See https://stackoverflow.com/questions/49195632/why-do-the-numpy-and-random-modules-give-different-random-numbers-for-the-same-s. Last accessed February 16, 2022.
- 7.
The documentation for the Numpy random package notes that the “high limit may be included in the returned array of floats due to floating-point rounding.” See https://numpy.org/doc/stable/reference/random/generated/numpy.random.uniform.html, last accessed March 14, 2022.
- 8.
Source for this example: https://stats.stackexchange.com/questions/374931/how-to-find-the-inverse-transform-of-the-gumbel-distribution. Last accessed February 16, 2022.
- 9.
The \(\leq \) is not needed in (9.10) because the probability at a specific value of X is zero. This is easy to see using (9.10) with both limits of the integral set to the same value, x.
- 10.
See https://medium.com/geekculture/the-story-behind-random-seed-42-in-machine-learning-b838c4ac290a, last accessed February 17, 2023, for an interesting perspective on 42.
- 11.
A military clock is the same, but by 24 h.
- 12.
Recall that 12 divides into 1 0 times with a remainder of 1.
- 13.
As of October 2020. See https://en.wikipedia.org/wiki/Mersenne_prime. Last accessed February 21, 2022.
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Paczkowski, W.R. (2023). Random Numbers: The Backbone of Stochastic Simulations. In: Predictive and Simulation Analytics. Springer, Cham. https://doi.org/10.1007/978-3-031-31887-0_9
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