Library for calculating statistical distributions, written in pure Python with zero dependencies.
Contribution: CONTRIBUTING.md
Documentation: README.md
- Binomial Distribution
- Chi-Squared Distribution
- Normal Distribution
- Poisson Distribution
- Geometric Distribution
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)
0.029656979029412885binomial.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)
0.9912362670526581binomial.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)
0.9912362670526581chi2.pdf(x, df)Probability density function for the chi-squared distribution X~X²(df),
where df is the degrees of the freedom.
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)
0.09357297231516998normal.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.
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)
0.9157737045522477normal.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)
0.9157737045522477poisson.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)
0.0019380401123575617poisson.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)
0.0034549033698374467poisson.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)
0.0034549033698374467geometric.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)
0.127208771geometric.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)
0.868127771geometric.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