Advanced search
Publication Cover
Journal of Statistics Education Volume 27, 2019 - Issue 1
Submit an article Journal homepage
3,607
Views
2
CrossRef citations to date
0
Altmetric
Articles

Symbulate: Simulation in the Language of Probability

Kevin RossStatistics Department, California Polytechnic State University, San Luis Obispo, CACorrespondence[email protected]
View further author information
&
Dennis L. SunStatistics Department, California Polytechnic State University, San Luis Obispo, CAView further author information
Pages 12-28 | Published online: 20 May 2019

Figures & data

Fig. 1 Output of P.sim(3), simulated outcomes of two four-sided dice rolls. (Note that Python uses zero-based indexing.)

Fig. 1 Output of P.sim(3), simulated outcomes of two four-sided dice rolls. (Note that Python uses zero-based indexing.)

Fig. 2 Approximate distribution of Y, the maximum of two four-sided dice rolls (table and plot).

Fig. 2 Approximate distribution of Y, the maximum of two four-sided dice rolls (table and plot).

Fig. 3 Approximate joint and marginal distributions of X and Y, the sum and maximum of two four-sided dice rolls.

Fig. 3 Approximate joint and marginal distributions of X and Y, the sum and maximum of two four-sided dice rolls.

Fig. 4 Sample paths of a Poisson process with rate parameter 1.

Fig. 4 Sample paths of a Poisson process with rate parameter 1.

Fig. 5 Approximate joint and marginal distributions of N(1.5), the process value at time 1.5, and T2, the time of the third arrival, for a rate 1 Poisson process N.

Fig. 5 Approximate joint and marginal distributions of N(1.5), the process value at time 1.5, and T2, the time of the third arrival, for a rate 1 Poisson process N.

Fig. 6 Ten sample paths of a simple symmetric random walk on the integers.

Fig. 6 Ten sample paths of a simple symmetric random walk on the integers.

Fig. 7 Kernel density plot of simulated values of X∼N(0,1).

Fig. 7 Kernel density plot of simulated values of X∼N(0,1).

Fig. 8 Simulated outcomes of independent dice rolls.

Fig. 8 Simulated outcomes of independent dice rolls.

Fig. 9 Simulated realizations of the event {Z>4}, where Z=X+Y, X and Y are independent, X∼Poisson(1), and Y∼Poisson(2).

Fig. 9 Simulated realizations of the event {Z>4}, where Z=X+Y, X and Y are independent, X∼Poisson(1), and Y∼Poisson(2).

Fig. 10 Approximate conditional distribution of X given {Z=5}.

Fig. 10 Approximate conditional distribution of X given {Z=5}.

Fig. 11 Log transform of a random variable with a Uniform(0,1) distribution.

Fig. 11 Log transform of a random variable with a Uniform(0,1) distribution.

Table 1 Comparison of Symbulate and R commands for the example illustrated in .

Fig. 12 Superimposed histograms.

Fig. 12 Superimposed histograms.

Fig. 13 Bivariate normal distribution: joint and marginal densities.

Fig. 13 Bivariate normal distribution: joint and marginal densities.

Fig. 14 Joint and joint conditional distributions for Example 2.

Fig. 14 Joint and joint conditional distributions for Example 2.

Fig. 15 Sample paths of an Ornstein–Uhlenbeck process.

Fig. 15 Sample paths of an Ornstein–Uhlenbeck process.

Table 2 Symbulate commands.

Table 3 Comparison across packages of syntax for a Normal(0, 1) distribution.

Fig. 16 Sampling distribution of the standardized sample mean, with a slider for n (n = 5 is displayed).

Fig. 16 Sampling distribution of the standardized sample mean, with a slider for n (n = 5 is displayed).

Table

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.