Response to Liang Hong and Ryan Martin on Their Comments on Our Paper Entitled, “Credibility Estimation of Distribution Functions with Applications to Experience Rating in General Insurance”

2016 ◽  
Vol 20 (1) ◽  
pp. 99-100
Author(s):  
Xiaoqiang Cai ◽  
Limin Wen ◽  
Xianyi Wu ◽  
Xian Zhou
Keyword(s):  
Distribution Functions ◽  
Experience Rating ◽  
General Insurance ◽  
Estimation Of Distribution

scholarly journals Estimating a Distribution Function at the Boundary

2020 ◽  
Vol 49 (1) ◽  
pp. 1-23
Author(s):  
Shunpu Zhang ◽  
Zhong Li ◽  
Zhiying Zhang
Keyword(s):  
Distribution Function ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Distribution Functions ◽  
Practical Application ◽  
Real World Applications ◽  
Distribution Kernel ◽  
Estimation Of Distribution ◽  
Simulation Results ◽  
Boundary Correction

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

scholarly journals On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Saddam Hussain ◽  
Mi Zichuan ◽  
Sardar Hussain ◽  
Anum Iftikhar ◽  
Muhammad Asif ◽  
...  
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Supplementary Information ◽  
Auxiliary Variables ◽  
Estimation Of Distribution

In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

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