Modeling
AtlasBrowse all 76
Menu
LearnProbabilityMechanisms, distributions, transformations, and limits.Bayesian learningPosterior updates, Thompson sampling, and Bayesian optimization.Deep learningActivations, likelihood-derived objectives, and the architectures built from them.01Activations02Likelihood to loss03ObjectivesSemi-supervisedUse a few labels and many unlabeled examples without hiding the assumptions.ReferenceDistributionsRelationship mapSource & method

Exponential

Waiting time to the next Poisson arrival; the continuous memoryless law.
Type continuousSupport x ≥ 0Family Waiting time
Probability densityf(x) = λe⁻λˣ
continuous

Exponential in motion

0.01.83.55.37.0
Supportx ≥ 0
Mean1
Variance1
Connections

Where the exponential
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

Geometric← time step→0

Scaled geometric waiting times converge to exponential waiting time.

Limiting resultGamma← α = 1

Gamma with shape one is exponential.

Special caseWeibullk = 1

Weibull with unit shape has constant hazard and is exponential.

Special caseUniform← −log U / λ

Inverse-transform sampling turns U(0,1) into Exp(λ).

Transformation

Zoom out

See every connection at once.

The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

Open the map