mc-tk 1.0.0

A Monte-Carlo toolkit for educational purposes

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.

future plan

gui.py - add a Flask or tk-inter (ttkbootstrap) GUI