discrete
Zipf
Power-law probabilities over ranks — the signature of word frequencies and city sizes.
Reference / Complete index
Seventy-six distributions.
One connected landscape.
Search every distribution represented in the source chart. Fourteen foundational models have a dedicated interactive page; every entry links back into the relationship material.
discrete
Discrete uniform
Equal chance on each of n outcomes: a fair die with any number of faces.
discrete
Rectangular
The discrete uniform under its classical name, flat across consecutive integers.
discrete
Beta-binomial
Binomial counts whose success rate is itself Beta-distributed — overdispersed by design.
discrete
Negative hypergeometric
Draws without replacement until a fixed number of failures arrives.
discrete
Zeta
Zipf stretched to infinite support, normalized by the Riemann zeta function.
discrete
Logarithmic
Heavy at one, thin in the tail — the count law behind species-abundance models.
discrete
Power series
The family umbrella: any count law whose probabilities come from a power-series expansion.
discreteinteractive
Poisson
Counts independent arrivals in a fixed exposure; a sparse-event limit of the binomial.
discreteinteractive
Binomial
The number of successes in n independent Bernoulli trials.
discrete
Hypergeometric
Successes in draws without replacement — quality control from a finite lot.
discreteinteractive
Bernoulli
One uncertain yes/no outcome—the atom from which binomial counts are built.
discrete
Beta-Pascal
Pascal waiting times whose success rate is itself Beta-distributed.
discrete
Gamma-Poisson
Poisson counts with a Gamma-random rate — the negative binomial in mixture form.
discreteinteractive
Geometric
Trials until the first success; the discrete memoryless law.
discrete
Pascal
Trials until the r-th success — the negative binomial counted from one.
discrete
Pólya
Urn draws that reinforce themselves; contagion added to the binomial.
discrete
Discrete Weibull
Weibull-shaped hazards on the integers, for lifetimes counted in cycles.
continuousinteractive
Normal
The central limit attractor and the default local model for additive noise.
continuous
Gamma-normal
The joint conjugate prior for a normal mean and precision together.
continuousinteractive
Standard normal
The parameter-free normal reached by standardizing X to (X−μ)/σ.
continuous
Arctangent
Defined by an arctangent CDF — a heavy-tailed relative of the Cauchy.
continuous
Hyperbolic secant
Bell-shaped like the normal but with heavier tails and closed-form everything.
continuousinteractive
Cauchy
A heavy-tailed ratio of normals; its mean and variance do not exist.
continuous
Inverse Gaussian
First-passage time of drifting Brownian motion; skewed, positive, tractable.
continuous
Standard Wald
The inverse Gaussian with its mean pinned at one.
continuous
Noncentral chi-square
Chi-square shifted by a noncentrality term; the power side of tests.
continuous
Chi
The square root of a chi-square — lengths of Gaussian vectors.
continuousinteractive
Chi-square
Sum of squared standard normals; a gamma special case central to inference.
continuous
Log-gamma
The logarithm of a gamma variate; extreme-value analysis on the log scale.
continuous
Inverted gamma
Reciprocal of a gamma — the conjugate prior for a normal variance.
continuous
Lognormal
Multiplicative noise made law: exponentiate a normal, get skewed positive data.
continuous
Generalized gamma
One shape knob away from exponential, Weibull, gamma, and lognormal at once.
continuousinteractive
Gamma
Positive sums and waiting time to multiple arrivals; contains exponential and chi-square.
continuous
Inverted beta
The Beta odds ratio p/(1−p); also known as the beta prime.
continuousinteractive
Beta
A flexible model for proportions and the conjugate prior for Bernoulli probability.
continuous
Arcsine
U-shaped on [0,1] — where random walks spend their time.
continuous
Makeham
Gompertz aging plus a constant background hazard; the actuarial mortality law.
continuous
Noncentral beta
Beta with a noncentrality shift, powering F-test calculations.
continuous
Standard Cauchy
Student t with one degree of freedom; no mean, no variance.
continuousinteractive
Student t
Normal uncertainty with an estimated scale; approaches normal as ν grows.
continuous
Hypoexponential
A chain of exponential stages with different rates — series systems.
continuous
Erlang
Sum of k exponential waits; the gamma with integer shape, born in telephone traffic.
continuous
Gompertz
Exponentially accelerating hazard — the demographer’s law of mortality.
continuous
Logistic-exponential
A two-parameter lifetime law that can bend its hazard both ways.
continuousinteractive
Exponential
Waiting time to the next Poisson arrival; the continuous memoryless law.
continuous
F
Ratio of two scaled chi-squares; the workhorse of analysis of variance.
continuous
Noncentral t
The t statistic under a false null; sample-size and power planning.
continuous
Doubly noncentral t
Noncentrality in both numerator and denominator of the t.
continuous
Hyperexponential
A mixture of exponentials, more variable than any single one.
continuous
Muth
A lifetime model whose hazard climbs steadily above the exponential baseline.
continuous
Error
The generalized normal: one shape parameter sweeps from spiky to near-uniform.
continuous
Standard uniform
Uniform on [0,1] — the raw material of every random-variate generator.
continuous
Exponential power
A lifetime law capable of bathtub-shaped hazards.
continuous
Minimax
Beta-like shapes with closed-form CDF and quantiles, built for order statistics.
continuous
Standard power
Power-function densities on the unit interval; Beta with one shape fixed.
continuous
Standard triangular
The tent on [−1, 1]: the sum of two uniforms.
continuous
Laplace
Back-to-back exponentials; the sparsity-inducing prior behind the lasso.
continuous
Pareto
The 80/20 tail: polynomial decay above a threshold.
continuous
IDB
Increasing, decreasing, or bathtub hazards from a single three-parameter law.
continuous
Rayleigh
Speeds of two-dimensional Gaussian vectors; Weibull with shape two.
continuous
Noncentral F
The F under an alternative hypothesis — ANOVA power analysis.
continuous
Doubly noncentral F
Noncentrality in both chi-squares of the F ratio.
continuousinteractive
Weibull
A lifetime model whose shape controls whether hazard rises, falls, or stays constant.
continuous
Log-logistic
Logistic on the log scale; heavy-tailed lifetimes with closed-form quantiles.
continuous
Benford
The law of leading digits: 1 appears about thirty percent of the time.
continuous
TSP
Two-sided power: the triangular generalized with a peak-sharpness exponent.
continuous
Power
A polynomial density rising toward the right end of its support.
continuousinteractive
Uniform
Equal density over an interval and the source of inverse-transform simulation.
continuous
von Mises
The normal of the circle: directional data with a concentration parameter.
continuous
Kolmogorov–Smirnov
Null law of the largest gap between empirical and true CDFs.
continuous
Triangular
Min, mode, max — the expert-elicitation stand-in for scarce data.
continuous
Logistic
Sigmoid CDF with slightly heavy tails; the link behind logistic regression.
continuous
Lomax
Pareto shifted to start at zero; long tails for incomes and failures.
continuous
Generalized Pareto
The tail law of exceedances over a threshold in extreme-value theory.
continuous
Extreme value
Limit law of maxima — Gumbel and friends for floods, records, and crashes.