Longest Run Of Heads

This repository contains a list of methods which calculate properties associated with the longest run of heads in a coin toss experiment. These functions are implementations of the methods described in [1]

Installation

Currently the only way to use this package is get the code from the LongestHeadRun.py file. If you use Github then you can clone the repository to obtain it by running

git clone https://github.com/JonnyCBB/LongestRunOfHeads.git

in the command prompt/terminal. Otherwise you can fork this repository or just copy and paste the Python code into a new .py file.

Usage

>>> import LongestHeadRun as lhr

# Find number of sequences of length 8 where the longest run of heads is 3 for
# a fair coin
>>> lhr.A_fair(8, 3)

# Calculate the probability of observing the number of sequences of length 8
# in which the longest run of heads does not exceed 3 in a coin toss sequence
# with a fair coin.
>>> lhr.prob_longest_head_run_fair(8, 3)

# Calculate the probability of observing the number of sequences of length 8
# in which the longest run of heads does not exceed 3 in a coin toss sequence
# with a biased coin. Probability of throwing heads is 0.75.
>>> lhr.prob_longest_head_run_fair(8, 3, 0.75)

You can generate a random coin toss sequence too.

# Simulate a coin toss sequence of length 10 with probability of heads 0.5
# (e.g. a fair coin).
>>> seq = lhr.generate_random_sequence(10, 0.5)

# From the sequence determine the longest run of Heads or Tails
>>> longest_run, value = lhr.determine_longest_run(seq)

# From the sequence determine the longest run of the specified value.
>>> longest_run, value = lhr.determine_longest_run(seq, heads_val="Head", only_heads=True)

All methods have been thoroughly documented using the Numpy style docstring format. So to get help just type help(some_method) where some_method is the name of a method in the file.

References

[1] Schilling, Mark F. "The longest run of heads." College Math. J 21.3 (1990): 196-207.