Estimation of an arbitrary mixture of uniform models
Let \(0=\theta_ 0<\theta_ 1<...<\theta_ k=1\) and let \(g_ i\) be the uniform density on \((\theta_ i,\theta_{i-1})\). Let \(X_ 1,...,X_ n\) be a sample from the mixture density \(f=\sum^{k}_{i=1}p_ if_ i\), where \(p_ i\geq 0\), \(\sum^{k}_{i=1}p_ i=1\). Equations for moment estimators are given (i) for the \(p_ i\) when the \(\theta_ i\) are known; (ii) for the \(\theta_ i\) when the \(p_ i\) are known; and (iii) for the \(p_ i\) and the \(\theta_ i\) when neither are known. Solutions are only presented in special cases.
scientific article; zbMATH DE number 3998979