---
title: "parameter"
type: concept
related: [Probability Distributions, Vector, Discrete Distribution, Probability, Parameter Learning]
source: https://www.jemoka.com/posts/kbhparameter/
confidence: high
status: active
---

a parameter of probability distribution govern the probabilities associated with different conditions in that distribution. It is usually a vector:
For instance, for uniform \(Uni(\alpha, \beta)\), parameter \(\theta = [\alpha, \beta]\).
importantly, for a discrete distribution system with 6 parameters, we only need 5 independent parameters to be able to satisfy the entire system. This is because a probability distribution must sum to 1.
however, for a conditional probability:
\begin{equation} p(x|a) \end{equation}
we need to specificity \((n-1)m\) parameters, whereby \(m\) is the number of states \(a\) can take, and \(n\) the number of states \(n\) can take. Each group of \(m\) has to add up to \(1\).
parameter learning see parameter learning
