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In survival or reliability studies, the quantile density function is an important characteristic in understanding the survival or aging process. In this various types of studies, a typical problem encountered in the data collection stage is that the samples may be censored from the right. In this article, we consider the problem of nonparametric estimation of a quantile density with right-censored data. A new adaptive wavelet estimator of this function is defined and its asymptotic properties are studied. In order to evaluate the performance of our estimator, small Monte Carlo simulations are carried out. Results show that the proposed estimators work well especially when the sample size is small and their calculations are simple. Finally, a real data example is provided.

An empirical estimate of quantile density function in presence of censoring