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Research draft

probability distribution

vr.tr.probability-distribution · XCT.QLT

Let an agent choose, fit and interpret probability distributions, explain their properties, compute probabilities, and avoid misapplication.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent choose, fit and interpret probability distributions, explain their properties, compute probabilities, and avoid misapplication.

A mathematical function describing the probabilities of possible outcomes of a random variable, either discrete, such as binomial and Poisson distributions, or continuous, such as normal, exponential, gamma and Gompertz distributions; distributions are characterised by parameters and moments and are the foundation of statistics and probabilistic modelling.

What it is for: Modelling uncertainty and variability.

It can be choose a distribution for data or a process; compute probabilities and quantiles; fit and test distributions; explain properties and relationships.

Distinguishing features

Assigns probabilities to outcomes

Discrete or continuous

Parametric families

Foundation of statistics

What it looks like

Not physical; curves, histograms and formulas.

How it is recognised

Probability mass or density functions

Parameters such as mean and variance

A histogram is data, not a distribution

Related models

is a kind of - category

probability measure

is a kind of - category

statistical model

uses - in discrete distributions

binomial coefficient

is related to - modelling

mathematical model

In practice

Families and kinds

discrete distributions

continuous distributions

multivariate distributions

heavy-tailed and survival distributions

flexible families such as metalog

Standards and regulation

ISO 3534 statistics vocabulary

Domain standards for risk modelling

Failure modes and hazards

Assuming normality wrongly

Ignoring heavy tails

Overfitting flexible families

Also called

Gompertz distributionMetalog distributionPanjer distributionLewandowski-Kurowicka-Joe distributioncentred probability distributionstandardized probability distributionexponential familyasymptotic distributionunimodal distributionmultivariate probability distributionheavy-tailed distributionsymmetric probability distributionzero-truncated Poisson distributionmixture distributionrelativistic Breit–Wigner distributiondistribution fittingjoint distribution of random variablesconditional probability distributionSub-Gaussian distributionAbsolutely continuous probability distributiondiscrete probability distributionmass distributionposterior probabilityprior probabilitymatrix variate distributionnoncentral beta distributionBenktander Gibrat distributionKent distributioninverse-gamma distributionrectified Gaussian distributioncompound Poisson distributionBirnbaum–Saunders distributionsingular distributionsampling distributionBenini distributionBenktander Weibull distributionCircular distributioncomplex normal distributioncompound probability distributionData generating process

+99

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Choose Selecting a distribution.

Match the process.

Process

Generating process.

Process

Generating process.

  1. Which distribution matches the process generating this data, such as counts, waiting times or proportions? definition
  2. Is the variable discrete or continuous? boundary

Tails

Tail behaviour.

Tails

Tails.

  1. Does the data show heavy tails or skew that rules out the normal distribution? boundary
  2. Which alternatives fit? action
Compute Probabilities.

Formulas and software.

Probability

Probabilities and quantiles.

Probability

Probabilities.

  1. What is the probability of this event or the quantile at this level under the distribution? measurement
  2. Which software function computes it? provenance

Moments

Mean and variance.

Moments

Moments.

  1. What are the mean, variance and other moments in terms of parameters? definition
  2. Do they exist for this distribution? boundary
Fit Estimation and testing.

Check the fit.

Estimate

Parameter estimation.

Estimate

Estimation.

  1. How are the parameters estimated from data, by maximum likelihood or other methods? action
  2. How uncertain are the estimates? measurement

Test

Goodness of fit.

Test

Goodness of fit.

  1. Does the distribution fit the data, according to plots and tests? measurement
  2. What are the limits of goodness-of-fit tests? boundary
Learn Understanding.

Relationships help.

Relations

Distribution relationships.

Relations

Relationships.

  1. How is this distribution related to others, such as limits and special cases? definition
  2. Where does it arise in theory? provenance

Teach

Teaching.

Teach

Teaching.

  1. How can this distribution be explained with simulations and examples? action
  2. Which misconceptions are common? provenance

What the second pass must settle

  • Should each distribution be a separate entry?
  • How should software implementations be linked?
  • How should fitting diagnostics be recorded?
Draft as JSON