Dist(ribution)s

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A set of quick reference and exploration utilities for choosing appropriate probability distributions for bayesian and other modeling using scipy, numpy, and pymc

• reference.md: table of key info for common probability distributions
• playground.ipynb: notebook with some interactive tools, including fine tuning distribution parameters, fitting a distribution to existing data, and fitting a distribution to an intuition or qualitative understanding of your problem
• Distribution Explorer, which is a fantastic resource for more specific/indepth info

Quick Reference Table

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name	values	bounds	parameters	models	preview
bernoulli	discrete	[0, 1]	p = probability of “success” outcome [0, 1]	binary outcome on single trial
beta	continuous	[0, 1]	α = n_successes+1 or shape 1, β = n_trials-α or shape 2	random variables between 0 and 1, probabilities & proportions
binomial	discrete	{1…n}	p = probability of “success” outcome per trial [0, 1], n = number of trials {1…n}	outcomes of multiple bernoulli trials
cauchy	continuous	(-inf, inf)	x0 = center of distribution, γ = scale (0, )	ratio between two independent, normal random variables with μ = 0
uniform	discrete	{a…b}	a = lower bound, b = upper bound	outcomes take limited integer values and are equally likely
uniform	continuous	[a, b]	a = lower bound, b = upper bound	outcomes take any value in range and are equally likely
exponential	continuous	[0, inf)	λ = rate of events in poisson process	time between poisson distributed events
gamma	continuous	(0, inf)	α = shape, β = rate	time between events ocurring at a constant average rate
gaussian	continuous	(-inf, inf)	μ = center of distribution, σ = standard deviation	normally distributed random variables
geometric	discrete	{0…inf}	p = probability of “success” outcome per trial [0, 1]	number of trials before 1 success
hypergeometric	discrete	{0…n}	p = probability of “success” outcome per trial [0, 1], n = number of trials {1…n}	successful outcomes from n trials
laplace	continuous	(-inf, inf)	μ = center of distribution, b = scale (0, )	difference between two independent exponential random variables with equal distributions
logistic	continuous	(-inf, inf)	μ = center of distribution, s = scale (0, )	log odds of randomly chosen probabilty in range [0, 1]
lognormal	continuous	[0, inf)	μ = center of distribution for random variable, σ = standard deviation for random variable	random variable with normally distributed ln
negative binomial	discrete	{0…inf}	p = probability of “success” outcome per trial [0, 1], r = number of successes {1…n}	number of failures before r successes
pareto	continuous	(x0, inf)	x0 = minimum x value (0, inf), α = shape (0, inf)	power law related variables
poisson	discrete	(0, inf)	λ = rate of events in given interval	number of events occurring in a fixed interval where events have a known average but variable occurence in the given interval
student t	continuous	(-inf, inf)	ν = degrees of freedom {1, inf}	generalized normal distribution with heavier tails
inverse gamma	continuous	(0, inf)	α = shape, β = scale	reciprocal of gamma distributed random variable
beta binomial	discrete	{1…n}	n = number of trials, α = shape 1, β = shape 2	binomial distribution for n trials where p is drawn from a beta(a, b) distribution