Python Probabilities 🐍

Library for accurate statistical calculations using Python.

• Binomial Distributions
  • Probability mass function
  • Cumulative distribution function
  • Inverse cumulative distribution function
• Normal Distributions
  • Probability density function
  • Cumulative distribution function
  • Inverse cumulative distribution function
• Poisson Distributions
  • Probability mass function
  • Cumulative distribution function
  • Inverse cumulative distribution
• Geometric Distributions
  • Probability mass function
  • Cumulative distribution function
  • Inverse cumulative distribution function

Binomial Distributions

Probability mass function

BinomialPD(r, n, p)

For the random variable X with the binomial distribution B(n, p), calculate the probability mass function.
Where r is the number of successes, n is the number of trials, and p is the probability of success.

Example
To calculate P(X=7) for the binomial distribution X~B(11, 0.33):

>>> from python_probabilities import BinomialPD
>>> BinomialPD(7, 11, 0.33)
0.029656979029412885

Cumulative distribution function

BinomialCD(r, n, p)

For the random variable X with the binomial distribution B(n, p), calculate the cumulative distribution function.
Where r is the number of successes, n is the number of trials, and p is the probability of success.

Example
To calculate P(X≤7) for the binomial distribution X~B(11, 0.33):

>>> from python_probabilities import BinomialCD
>>> BinomialCD(7, 11, 0.33)
0.9912362670526581

Inverse cumulative distribution function

InvBinomialCD(q, n, p)

For the random variable X with the binomial distribution B(n, p), calculate the inverse for the cumulative distribution function.
Where q is the cumulative probability, n is the number of trials, and p is the probability of success.

InvBinomialCD(q, n, p) returns the smallest integer x such that BinomialCD(x, n, p) is greater than or equal to q.

Example
To calculate the corresponding value for r (the number of successes) given the value for q (the cumulative probability):

>>> from python_probabilities import BinomialCD, InvBinomialCD
>>> InvBinomialCD(0.9912362670526581, 11, 0.333)
7
>>> BinomialCD(7, 11, 0.333)
0.9912362670526581

Normal Distributions

Probability density function

NormalPD(x, µ, σ)

Probability density function for the normal distribution X~N(µ, σ).
Where µ is the mean, and σ is the standard deviation.

Cumulative distribution function

NormalCD(x, µ, σ)

Cumulative distribution function for the normal distribution X~N(µ, σ).
Where µ is the mean, and σ is the standard deviation.

Example
To calculate P(X≤0.891) for the normal distribution X~N(0.734, 0.114):

>>> from python_probabilities import NormalCD
>>> NormalCD(0.891, 0.734, 0.114)
0.9157737045522477

Inverse cumulative distribution function

InvNormalCD(y, µ, σ)

Inverse cumulative distribution function for the normal distribution X~N(µ, σ).
Where µ is the mean, and σ is the standard deviation.

InvNormalCD(y, µ, σ) returns the smallest integer x such that NormalCD(x, µ, σ) is greater than or equal to y.

Example
To calculate the corresponding value for x given the value for y:

>>> from python_probabilities import NormalCD, InvNormalCD
>>> InvNormalCD(0.9157737045522477, 0.734, 0.114)
0.891
>>> NormalCD(0.891, 0.734, 0.114)
0.9157737045522477

Poisson Distributions

Probability mass function

PoissonPD(r, m)

For the random variable X with the poisson distribution Po(m), calculate the probability mass function.
Where r is the number of occurrences, and m is the mean rate of occurrence.

Example
To calculate P(X=7) for the poisson distribution X~Po(11.556):

>>> from python_probabilities import PoissonPD
>>> PoissonPD(11, 23.445)
0.0019380401123575617

Cumulative distribution function

PoissonCD(r, m)

For the random variable X with the poisson distribution Po(m), calculate the cumulative distribution function.
Where r is the number of occurrences, and m is the mean rate of occurrence.

Example
To calculate P(X≤7) for the poisson distribution X~Po(11.556):

>>> from python_probabilities import PoissonCD
>>> PoissonCD(11, 23.445)
0.0034549033698374467

Inverse cumulative distribution

InvPoissonCD(q, m)

For the random variable X with the poisson distribution Po(m), calculate the inverse for the cumulative distribution function.
Where q is the cumulative probability, and m is the mean rate of occurrence.

InvPoissonCD(q, m) returns the smallest integer x such that PoissonCD(x, m) is greater than or equal to q.

Example
To calculate the corresponding value for r (number of occurrences) given the values for q (cumulative probability):

>>> from python_probabilities import PoissonCD, InvPoissonCD
>>> InvPoissonCD(0.0034549033698374467, 23.445)
11
>>> PoissonCD(11, 23.445)
0.0034549033698374467

Geometric Distributions

Probability mass function

GeometricPD(x, p)

Probability mass function for the geometric distribution X~G(p).
Where x is the number of trials before the first success, and p is the probability of success.

Example
To calculate P(X=3) for the geometric distribution X~G(0.491):

>>> from python_probabilities import GeometricPD
>>> GeometricPD(3, 0.491)
0.127208771

Cumulative distribution function

GeometricCD(x, p)

Cumulative distribution function for the geometric distribution X~G(p).
Where x is the number of trials before the first success, and p is the probability of success.

Example
To calculate P(X≤3) for the geometric distribution X~G(0.491):

>>> from python_probabilities import GeometricCD
>>> GeometricCD(3, 0.491)
0.868127771

Inverse cumulative distribution function

InvGeometricCD(area, p)

Inverse cumulative distribution function for the geometric distribution X~G(p).
Where x is the number of trials before the first success, and p is the probability of success.

InvGeometricCD(area, p) returns the smallest integer x such that GeometricCD(x, p) is greater than or equal to area.

Example
To calculate the corresponding value for x given the value for area:

>>> from python_probabilities import GeometricCD, InvGeometricCD
>>> InvGeometricCD(0.868, 0.491)
3
>> GeometricCD(3, 0.491)
0.868127771