Research Article Open Access

A Suggested Nonparametric Bivariate Logistic Density Estimator with Application on the Productivity of Egyptian Wheat during 2019/2020

Samah M. Abo-El-Hadid1
  • 1 Helwan University, Egypt

Abstract

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.

Journal of Mathematics and Statistics
Volume 17 No. 1, 2021, 44-49

DOI: https://doi.org/10.3844/jmssp.2021.44.49

Submitted On: 14 April 2021 Published On: 27 May 2021

How to Cite: Abo-El-Hadid, S. M. (2021). A Suggested Nonparametric Bivariate Logistic Density Estimator with Application on the Productivity of Egyptian Wheat during 2019/2020. Journal of Mathematics and Statistics, 17(1), 44-49. https://doi.org/10.3844/jmssp.2021.44.49

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Keywords

  • Joint Kernel Density Estimator
  • Bivariate Logistic Kernel
  • Optimal Bandwidth