NONPARAMETRIC KERNEL DISTRIBUTION FUNCTION ESTIMATION NEAR ENDPOINTS

In this paper, two kernel cumulative distribution function estimators are introduced and investigated in order to improve the boundary effects, we will restrict our attention to the right boundary. The first estimator uses a self-elimination between modify theoretical Bias term and the classical kernel estimator itself. The basic technique of construction the second estimator is kind of a generalized reflection method involving reflection a transformation of the observed data. The theoretical properties of our estimators turned out that the Bias has been reduced to the second power of the bandwidth, simulation studies and two real data applications were carried out to check these phenomena and are conducted that the proposed estimators are better than the existing boundary correction methods.

Finite Population Distribution Function Estimation Using Auxiliary Information Under Simple Random Sampling

In this paper, a new estimator for estimating the finite population distribution function(DF) are propose using supplementary information on the DF of the auxiliary variable under simple random sampling. A comparative study is conducted to compare, theoretically and numerically, the adapted distribution function estimators of Cochran (1940), Murthy (1967), Bahl and Tuteja (1991), Rao (1991), Singh et al. (2009) and Grover and Kaur (2014) with the proposed estimators. It is found that the proposed estimators always perform better than the adapted estimators in terms of MSE and percentage relative efficiency.