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Journal of Sciences Islamic Republic of Iran، جلد ۳۳، شماره ۱، صفحات ۴۵-۵۴
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عنوان انگلیسی Estimating Cumulative Distribution Function Using Gamma Kernel
چکیده انگلیسی مقاله 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.
کلیدواژه‌های انگلیسی مقاله Asymmetric kernels,cumulative distribution,boundary problem,almost sure convergence
نویسندگان مقاله Behzad Mansouri |
Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran

Sami Atiyah Sayyid Al-Farttosi |
Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran

Habiballah Mombeni |
Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran

Rahim Chinipardaz |
Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran

نشانی اینترنتی https://jsciences.ut.ac.ir/article_85043_e13a2cd04cc2c6d11950582655309fe0.pdf
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