On a Class of Estimates of the Probability Density Function and mode based on a Random Number of Observations

The estimate of the probability density function, based on a fixed number of observations, studied by Yamato (1971) and Davies (1973), has been extended to the case when the number of observations is random. Asymptotic properties of the estimates of She d:osity function and its derivatives, as also of the estimate of the mode, have been studied under appropriate conditions.