THE TRANSFORMED KERNEL ESTIMATION AND ITERATIVE ALGORITHM

Let X₁,…,X_nbe i.i.d. random with density functionf（x）, which has the shape of a steep head and a heave tail such as log-normal and Weibull density function. Consider a transformation T:Y_i=T（X_i）, where Y_i obey a density function g（y） which has a minimum error of estimate. The estimatef（x）can be obtained byf（x）= T'（x）g(T（x）). In this paper we present a iterative algorithm of the transformed kernel estimate and discuss the performance of estimate. A Monte Carlo simulations show that the transformed kernel estimate is suitable for the estimate of log-normal and Weibull density function.