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Mansouri, Behzad, Atiyah Sayyid Al-Farttosi, Sami, Mombeni, Habiballah, Chinipardaz, Rahim. (1400). Estimating Cumulative Distribution Function Using Gamma Kernel. , 33(1), 45-54. doi: 10.22059/jsciences.2021.324868.1007652
Behzad Mansouri; Sami Atiyah Sayyid Al-Farttosi; Habiballah Mombeni; Rahim Chinipardaz. "Estimating Cumulative Distribution Function Using Gamma Kernel". , 33, 1, 1400, 45-54. doi: 10.22059/jsciences.2021.324868.1007652
Mansouri, Behzad, Atiyah Sayyid Al-Farttosi, Sami, Mombeni, Habiballah, Chinipardaz, Rahim. (1400). 'Estimating Cumulative Distribution Function Using Gamma Kernel', , 33(1), pp. 45-54. doi: 10.22059/jsciences.2021.324868.1007652
Mansouri, Behzad, Atiyah Sayyid Al-Farttosi, Sami, Mombeni, Habiballah, Chinipardaz, Rahim. Estimating Cumulative Distribution Function Using Gamma Kernel. , 1400; 33(1): 45-54. doi: 10.22059/jsciences.2021.324868.1007652

Estimating Cumulative Distribution Function Using Gamma Kernel

Journal of Sciences, Islamic Republic of Iran
مقاله 4، دوره 33، شماره 1، خرداد 2022، صفحه 45-54    اصل مقاله (373.02 K)
نوع مقاله: Original Paper
شناسه دیجیتال (DOI): 10.22059/jsciences.2021.324868.1007652
نویسندگان
Behzad Mansouri* ؛ Sami Atiyah Sayyid Al-Farttosi؛ Habiballah Mombeni؛ Rahim Chinipardaz
Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran
چکیده
In this article, we propose the gamma kernel estimator for the cumulative distribution functions with nonnegative support. We derive the asymptotic bias and variance of the proposed estimator in both boundary and interior regions and show that it is free of boundary bias. We also obtain the optimal smoothing parameter which minimizes the mean integrated square error (MISE). In addition to consistency, we prove the almost sure convergence of the proposed estimator and show that it follows the same approximate normal distribution as empirical distribution. We presented a simulation study to compare the performance of the proposed estimator with other estimators. We use the proposed estimator to estimate the cumulative probability distribution function of the food expenses for urban households in Iran.
کلیدواژه‌ها
Asymmetric kernels؛ Cumulative distribution؛ Boundary problem؛ Almost sure convergence
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