Promethium 🐍

Library for calculating statistical distributions, written in pure Python with zero dependencies.

Contribution: CONTRIBUTING.md

Documentation: README.md

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Documentation

• Binomial Distribution
  • Probability mass function
  • Cumulative distribution function
  • Inverse cumulative distribution function
• Chi-Squared Distribution
  • Probability density function
  • Cumulative distribution function
• Normal Distribution
  • Probability density function
  • Cumulative distribution function
  • Inverse cumulative distribution function
• Poisson Distribution
  • Probability mass function
  • Cumulative distribution function
  • Inverse cumulative distribution
• Geometric Distribution
  • Probability mass function
  • Cumulative distribution function
  • Inverse cumulative distribution function

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Binomial Distribution

Probability mass function

binomial.pmf(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 promethium import binomial
>>> binomial.pmf(7, 11, 0.33)
0.029656979029412885

Cumulative distribution function

binomial.cdf(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 promethium import binomial.cdf
>>> binomial.cdf(7, 11, 0.33)
0.9912362670526581

Inverse cumulative distribution function

binomial.ppf(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.

binomial.ppf(q, n, p) returns the smallest integer x such that binomial.cdf(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 promethium import binomial
>>> binomial.ppf(0.9912362670526581, 11, 0.333)
7
>>> binomial.cdf(7, 11, 0.333)
0.9912362670526581

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Chi-Squared Distribution

Probability density function

chi2.pdf(x, df)

Probability density function for the chi-squared distribution X~X²(df), where df is the degrees of the freedom.

Cumulative distribution function

chi2.cdf(x, df)

Cumulative distribution function for the chi-squared distribution X~X²(df), where df is the degrees of the freedom.

Example
To calculate P(0≤X≤0.556) for the chi-squared distribution X~X²(3):

>>> from promethium import chi2
>>> chi2.cdf(0.556, 3)
0.09357297231516998

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Normal Distribution

Probability density function

normal.pdf(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

normal.cdf(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 promethium import normal
>>> normal.cdf(0.891, 0.734, 0.114)
0.9157737045522477

Inverse cumulative distribution function

normal.ppf(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.

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

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

>>> from promethium import normal
>>> normal.ppf(0.9157737045522477, 0.734, 0.114)
0.891
>>> normal.cdf(0.891, 0.734, 0.114)
0.9157737045522477

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Poisson Distribution

Probability mass function

poisson.pmf(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 promethium import poisson
>>> poisson(11, 23.445)
0.0019380401123575617

Cumulative distribution function

poisson.cdf(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 promethium import poisson
>>> poisson.cdf(11, 23.445)
0.0034549033698374467

Inverse cumulative distribution

poisson.ppf(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.

poisson.ppf(q, m) returns the smallest integer x such that poisson.cdf(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 promethium import poisson
>>> poisson.ppf(0.0034549033698374467, 23.445)
11
>>> poisson.cdf(11, 23.445)
0.0034549033698374467

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Geometric Distribution

Probability mass function

geometric.pmf(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 promethium import geometric
>>> geometric.pmf(3, 0.491)
0.127208771

Cumulative distribution function

geometric.cdf(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 promethium import geometric
>>> geometric.cdf(3, 0.491)
0.868127771

Inverse cumulative distribution function

geometric.ppf(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.

geometric.ppf(area, p) returns the smallest integer x such that geometric.cdf(x, p) is greater than or equal to area.

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

>>> from promethium import geometric
>>> geometric.ppf(0.868, 0.491)
3
>> geometric.cdf(3, 0.491)
0.868127771