A little python to alleviate math programming

Smital Desai

Hello Pythonistas , In this blog post we are trying to see how can we represent the mathematical formula that uses summation notation in Python. I am not really a math lover so whenever i see something represented in this kind of formula , i get nervous about whether i will be able to handle it or not.

Gini Coefficient

This excerpt has been taken from Economics simulation.

As seen in the formula , i goes from 1 to n which can be done using for loop ** for i in range(n) ** for numerator , we can see that for each i we are performing ** ( i * y[i] ) and finally there is sum() function which is replacing the sigma.

for the denominator we are not doing any alteration on each iteration we can simply invoke sum() on y

def gini(y):
   "Compute the Gini coefficient (a measure of equality/inequality) in a population, y."
   y = sorted(y)
   n = len(y)
   numer = 2 * sum((i) * y[i] for i in range(1, n))
   denom = n * sum(y)
   return (numer / denom) - (n + 1) / n

Chained comparisons

In [2]: x = 10

In [3]: y = 20

In [4]: 15 > x and 15 < y
Out[4]: True

In [5]: x < 15 < y
Out[5]: True

Simulating Roulle spins

How to perform Six roulette wheel spins (weighted sampling with replacement) There are 18 Red slots , 18 black slots and 6 green slots. .. code:: python
 

>>> from random import *
>>> choices(['red', 'black', 'green'], [18, 18, 2], k=6)
['red', 'green', 'black', 'black', 'red', 'black']

Biased Coins

This excerpt has been taken from Random module documentation

 >>> # Estimate the probability of getting 5 or more heads from 7 spins
 >>> # of a biased coin that settles on heads 60% of the time.
 >>> trial = lambda: choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5
>>> sum(trial() for i in range(10000)) / 10000
    0.4169

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