TITLE:
Density Estimation Using Gumbel Kernel Estimator
AUTHORS:
Javaria Ahmad Khan, Atif Akbar
KEYWORDS:
Asymmetrical Kernels, Boundary Problems, Density Estimation, Flood Data, Gumbel Kernel Estimator
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.2,
April
22,
2021
ABSTRACT: In this article, our proposed kernel estimator, named as Gumbel kernel,
which broadened the class of non-negative, asymmetric kernel density
estimators. Such kernel estimator can be used in nonparametric estimation of
the probability density function (pdf).
When the density functions have limited bounded support on [0, ∞) and they are
liberated of boundary bias, always non-negative and obtain the optimal rate of
convergence for the mean integrated squared error (MISE). The bias, variance
and the optimal bandwidth of the proposed estimators are investigated on
theoretical grounds as well as on simulation basis. Further, the applicability of
the proposed estimator is compared to Weibull kernel
estimator, where performance of newly proposed kernel is outstanding.