economet

#!/bin/python3


"""
returns possible combinatations in a list
"""
def combo(n,k):
    import itertools
    return list(itertools.combinations(list(range((n-(n-1)),(n+1))),k))



"""
returns a tuple representing entire sample space of a given DICT
"""
def sample_space(inputs):
    rslt = []
    for k in inputs:
        rslt +=  k * inputs[k]
    return(tuple(rslt))


"""
retuns number of outcomes of an event. requires sample space(ss) and
number times sample is taken
"""

def outcomes(ss, taken):
    import math
    n = len(ss)
    return math.factorial(n)  /  (math.factorial(taken) * math.factorial(n - taken))



"""
retuns relative frequency (Na) for a given event. Requires event and population
"""
def relative_freq(pop, event):
    rslts = 1
    for k in event[1]:
        rslts *= len(combo(pop[k],event[1][k]))
    return(round(rslts, 3))



"""
retuns boolean value if first index of tuple matches total of second
"""
def validate_event(input):
    ttl = 0
    for k in input[1]:
        ttl += input[1][k]
    return(input[0] == ttl)


"""
return probability of an event
requires a population description DICT {desceet value: qty}
and event criteria TUPLE  <num of event, {criteria:dict}
"""

def prob(pop, event):
    if (validate_event(event)):
        Na = relative_freq(pop,event)
        N = outcomes(sample_space(pop), event[0])
        return(round(Na/N, 3))
    else:
        print("Error: Please check event input")