A note on a consistent estimator of a mixing distribution function

Summary In this note, we will study a consistent estimator of a mixing distribution function (mixing d.f.). The estimator discussed in this note is that of Choi and Bulgren [4]. Since there is some doubt about the way of proving Lemma in [4] which is used for showing the consistency of the estimator in [2], [3] and [4], we will give different lemmas. We will show that their result (which is still true by using our lemmas) holds under a weaker assumption than theirs. The existence of the estimator is not discussed in [4]. So, we will give conditions under which the existence is guaranteed. The research was supported in part by Scientific Research Fund from the Ministry of Education of Japan. No. 564076.