Kernel density estimation is a standard method for estimating the probability density function, which in many cases works
 well. However, it has been found that it does not work well for negative, sloping, and wide-tail distributions, which are
 commonfeatures of the distribution of longevity, income, and so on. The purpose of this paper is to evaluate the performance
 of multiplicative bias correction (MBC) methods using asymmetric kernel estimators and compare this estimator with other
 boundary problem solving methods. In this paper, in addition to introducing MBC methods in combination with asymmetric
 kernel estimators, a simulation study shows that this estimator can, in some cases, provide a much better fit for density
 estimation than the standard kernel estimator. MBC methods using asymmetric kernel estimators were also used to estimate
 the lifetime density of transplanted corneas in 119 patients.