Introduction

This library helps simulate probability problems, with a focus on conditional probability. You can also use it to create custom single or joint distributions, define your own PMF or PDF, and generate probability tables and sample data.

Installation

pip install pprobs

Probability Simulator

It simulates probability theory problems, especially conditional probability.

Example 1

We want to get some information by defining some events.

• P(A) = 0.3
• P(B) = 0.2
• P(A^B) = 0.1
• A and B are dependent
• P(A+B) = ? , P(A|B) = ?

from pprobs.simulation import Simulator

space = Simulator()

space.add_event('A', 0.3)
space.add_event('B', 0.2)
space.add_event('A^B', 0.1)

prob_1 = space.get_prob('A+B') # A+B means union of A and B
prob_2 = space.get_prob('A|B')

print(prob_1, prob_2) # 0.4  0.5

Example 2

In a group of 100 sports car buyers, 40 bought alarm systems, 30 purchased bucket seats, and 20 purchased an alarm system and bucket seats. If a car buyer chosen at random bought an alarm system, what is the probability they also bought bucket seats?

By Statisticshowto

• P(SEAT) = 0.3
• P(ALARM) = 0.4
• P(SEAT ^ ALARM) = 0.2
• P(SEAT | ALARAM) = ?

from pprobs.simulation import Simulator

space = Simulator()

space.add_event('SEAT', 0.3).add_event('ALARM', 0.4) # We can also add events sequentially in a line (chaining) 
space.add_event('SEAT^ALARM', 0.2) # A^B means intersection of A & B

print(space.get_prob('SEAT|ALARM')) # 0.5

Example 3

Totaly 1% of people have a certain genetic defect.90% of tests for the gene detect the defect (true positives). 9.6% of the tests are false positives. If a person gets a positive test result, what are the odds they actually have the genetic defect?

By Statisticshowto

• P(GEN_DEF) = 0.01
• P(POSITIVE|GEN_DEF) = 0.9
• P(POSITIVE|GEN_DEF!) = 0.096
• P(GEN_DEF|POSITIVE) = ?

space = Simulator()

space.add_event('GEN_DEF', 0.01)
space.add_event('POSITIVE|GEN_DEF', 0.9) # A|B means A given B
space.add_event('POSITIVE|GEN_DEF!', 0.096) # A! means complement of A

print(space.get_prob('GEN_DEF|POSITIVE')) # 0.0865

Example 4

Bob has an important meeting tomorrow and he has to reach the office on time in the morning. His general mode of transport is by car and on a regular day (no car trouble) the probability that he will reach on time is 0.3. The probability that he might have car trouble is 0.2. If the car runs into trouble he will have to take a train and only 2 trains out of the available 10 trains will get him to the office on time.

By Hackerearth

• P(ON_TIME|CAR_OK) = 0.3
• P(ON_TIME|CAR_OK!) = 2/10 => Go by train
• P(CAR_OK!) = 0.2
• P(ON_TIME) = ?

space = Simulator()

space.add_event('ON_TIME|CAR_OK', 0.3)
space.add_event('ON_TIME|CAR_OK!', 2/10)
space.add_event('CAR_OK!', 0.2)

prob = space.get_prob('ON_TIME') # Probability of ON_TIME

print(prob) # 0.28

Distribution Simulator

It is useful to create a custom single or joint distribution with a specific PMF or PDF to get a probability table and generate data based on a probability function.

Example 1

Suppose that we have a discrete random variable with a specific PMF. We want to generate many data based on this variable. As you see in the second example 1 has the largest probability and duplicates more and 4 has the smallest probability and duplicates less.

from pprobs.distribution import Discrete

# First 
def pmf(x):
    return 1 / 6

dist = Discrete(pmf, [1, 2, 3, 4, 5, 6]) # The second is the sample space of our PMF

print(dist.generate(15)) # [4, 3, 1, 6, 5, 3, 5, 3, 5, 4, 2, 5, 6, 1, 6]


# Second
def pmf(x):
    return 1 / x

dist = Discrete(pmf, [1, 2, 3, 4])
print(dist.generate(15)) # [1, 2, 1, 1, 1, 4, 3, 1, 1, 3, 2, 4, 1, 2, 2]

Example 2

Suppose that we have a continuous random variable with a specific PDF.

from pprobs.distribution import Continuous

def pdf(x):
  if x > 1:
    return x / x ** 2
  return 0

dist = Continuous(pdf, [1, 6]) # The second is the sample interval of our PDF

print(dist.generate(15)) # [2.206896551724138, 4.103448275862069, ..., 5.655172413793104, 6.0]

Example 3

Suppose that we have a Continuous Joint variable with a specific PDF.

from pprobs.distribution import Joint

def pdf(x, y):
  if x > 1:
    return 1 / (x * y)
  return 0

dist = Joint(pdf, [1, 6], [3, 10]) # The second and third are the intervals of our PDF

print(dist.probability_table(force=20)) # if force gets more, many number will generate

Output:

X/Y	x=3.0	X=3.7	...	X=10
X=1.0	0.000	0.000	...	0.000
...	...	...	...	...
X=6.0	0.055	0.044	...	0.016

print(dist.get_prob(3.5, 3.5)) # 0.081 is P(X=3.5, Y=3.5)
print(dist.get_prob([1, 6], 4)) # 0.041 is P(Y=4) because X includes its whole domain
print(dist.get_prob(2.1, [1, 4])) # 0.206 is P(X=2.1, Y in [1, 4])

Example 4

Suppose that we have a Discrete Joint variable with a specific PMF.

from pprobs.distribution import Joint

def pmf(x, y):
  if x > 1:
    return 1 / (x * y)
  return 0

dist = Joint(pmf, range(1, 6), range(6, 10)) # The second and third are the sample space of our PMF

print(dist.probability_table()) 

Output:

X/Y	Y=6	Y=7	Y=8	Y=9
X=1	0.000000	0.000000	0.000000	0.000000
X=2	0.083333	0.071429	0.062500	0.055556
X=3	0.055556	0.047619	0.041667	0.037037
X=4	0.041667	0.035714	0.031250	0.027778
X=5	0.033333	0.028571	0.025000	0.022222

print(dist.get_prob(2, range(6, 10))) # 0.272 is P(X=2)
print(dist.get_prob(2, 6)) # 0.083 is P(X=2, Y=6)

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