TY  - JOUR
AU  - Abo-El-Hadid, Samah M. 
PY  - 2021
TI  - A Suggested Nonparametric Bivariate Logistic Density Estimator with Application on the Productivity of Egyptian Wheat during 2019/2020
JF  - Journal of Mathematics and Statistics
VL  - 17
IS  - 1
DO  - 10.3844/jmssp.2021.44.49
UR  - https://thescipub.com/abstract/jmssp.2021.44.49
AB  - In this study, the nonparametric standard logistic density estimator, introduced by Abo-El-Hadid (2018), is extended to the bivariate case. The multiplicative standard logistic distribution is used as a kernel function to derive the bivariate kernel estimator. The statistical properties of the resulting estimator are studied, which are: The asymptotic bias, variance, Mean Squared Error (MSE) and Integrated Mean Squared Error (IMSE); also, the optimal bandwidth is obtained. A simulation study is introduced to investigate the performance of the proposed estimator with other estimators. We also apply the proposed estimator to a real data set to estimate the bivariate density of the planted and productive areas of wheat in Egypt.