Nonparametric Bayes estimation of a distribution under nominationsampling

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some distribution. If the data are {(Y_i, K_i), i =1, . . ., n} where K_i is the size of sample i, and Y_i is the maximum of a random sample of size K_i from an unknown Cdf, F; the Bayes estimator of F is derived by discretizing F over a fixed finite partition of the support of F and taking a Dirichlet distribution as the prior for the probabilities of the partitioning intervals. For the flood data of the Nidd River considered by R.A. Boyles and F.J. Samaniego (J. Am. Stat. Assoc., vol.81, p.1039-45, 1986), the plots of the Bayes estimator of F are obtained for several sets of values of the parameters of the Dirichlet distribution