mc-tk
A Monte-Carlo toolkit for educational purposes.
pip install mc-tk
package architecture
experiments
- classical / typical experiments in probability
distributions
- inclulde MC experiments that produce common distributions
samplings
- sampling distributions of statistic used in hypothesis tests
modules and classes
| Module | Class | Description |
| mc.experiments | Pi | Perform Buffon’s needle experiment to estimate π . |
| Parcel | Simulate a bi-directional parcel passing game. | |
| Dices | Estimate the probabilities of various dice combinations. | |
| Prisoners asymptotic_analysis() | The famous locker puzzle(100-prisoner quiz). And the asymptotic_analysis() function will prove that the survival chance limit is 1−ln2 when n approaches +∞ . | |
| Galton_Board | Use the classic Galton board experiment to produce a binomial distribution. | |
| Paper_Clips | Use the paper clip experiment to produce a Zipf distribution. | |
| Sudden_Death | This class simulates a sudden death game to produce the exponential distribution. | |
| mc.distributions | Poisson | This class will demonstrate that Poisson is a limit distribution of b(n,p) when n is large, and p is small. |
| Benford | Verify Benford’s law using real-life datasets, including the stock market data, international trade data, and the Fibonacci series. | |
| mc.samplings | Clt | Using various underlying distributions to verify the central limit theorem. This class provides the following underlying distributions. |
| ’uniform’ - a uniform distribution U(-1,1). | ||
| ’expon’- an exponential distribution Expon(1). | ||
| ’poisson’ - poisson distribution π(1). | ||
| ’coin’- Bernoulli distribution with p = 0.5. | ||
| ’tampered_coin’ - PMF:{0:0.2,1:0.8}, i.e., head more likely than tail. | ||
| ’dice’- PMF:{1:1/6,2:1/6,3:1/6,4:1/6,5:1/6,6:1/6}. | ||
| ’tampereddice’ - PMF: {1:0.1,2:0.1,3:0.1,4:0.1,5:0.1,6:0.5},i.e., 6 is more likely. | ||
| T_Test | This class constructs an r.v. (random variable) following the t distribution. | |
| Chisq_Gof_Test | Verify the statistic used in Pearson’s Chi-Square Goodness-of-Fit test follows the χ2 distribution. | |
| Fk_Test | Verify the Fligner-Killeen Test statistic(FK) follows the χ2 distribution. | |
| Bartlett_Test | Verify the Bartlett’s test statistic follows the χ2 distribution. | |
| Anova | Verify the statistic of ANOVA follows the F distribution. | |
| Kw_Test | Verify the Kruskal-Wallis test statistic (H) is a χ2 r.v. | |
| Sign_Test | For the sign test (medium test), verify its N- and N+ statistics both follow b(n,1/2). | |
| Cochrane_Q_Test | Verify the statistic T in Cochrane-Q test follows the χ2 distribution. | |
| Hotelling_T2_Test | Verify the T2 statistic from two multivariate Gaussian populations follows the Hotelling’s T2 distribution. |
This version is major upgrade on the original version.
All the functions were refactored by the OOP (Object Oriented Programming) pattern.
McBase acts as a common base class for all MC derivative classes.
publication
doc
future plan
gui.py - add a Flask or tk-inter (ttkbootstrap) GUI
1 maintainer
Metadata
1 maintainer
Release files for mc-tk 1.1.0
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