ABSTRACT
Parametric statistics concerns parametrised families of probability distributions p(θ), where the parameter θ = (θ 1,…, θ d ) varies over some open set in R d . The most common example is the normal family, which is usually expressed as a family of densities p ( μ , σ ) = N ( μ , σ 2 ) = 1 2 π σ exp ( − ( x − μ ) 2 2 σ 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141268/7ec67f00-5aa3-4444-a5a8-38b4589858e0/content/eq1.tif"/> The parameter θ in this case is the pair (μ, σ) which varies over the open subset of R 2 determined by μ > 0. The sample space is R and the densities are with respect to Lebesgue measure dx on R, so that as a set of probability measures the normal family is N = { p ( μ , σ ) d x | μ ∈ R , σ > 0 } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141268/7ec67f00-5aa3-4444-a5a8-38b4589858e0/content/eq2.tif"/>
