Estimating a distribution function based on minima-nomination sampling
Martin T. Wells, Ram Chandra Tiwari · Lecture notes-monograph series · 1990
The nonparametric maximum likelihood estimator of a distribution function based on a maxima-nomination sample has been derived recently by Boyles and Samaniego (1986).In this article we study minima-nominations for the case of censored data. Introduction.Let X i,... ,X z χ., i = 1,..., n be independent identically distributed (i.i.d.) random variables (r.v.'s) having a common continuous distribution function F with support (0,oo).Denote the vector (Xα,... ,X t A^) by X t , i = 1,.. .,n.Define the map Π t : IR At -> IR such that Π t maps X; into a particular element in X t , say X{ (i -1,.. .,ft).We shall call X t the nominee of X t and the collection {X t : i = 1,.. .,n} is called the nomination sample.The case when Tίi(X.i) = maxi<j</^.X t j has been studied by Willemain (1980) and Boyles and Samaniego (1986).Another important case is where Π^X;) = minκj