Library for accurate statistical calculations using Python.
Project description
Python Probabilities 🐍
Library for accurate statistical calculations using Python.
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
InvBinomial(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
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
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