کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1147661 957783 2011 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A fractional order statistic towards defining a smooth quantile function for discrete data
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A fractional order statistic towards defining a smooth quantile function for discrete data
چکیده انگلیسی

This work is motivated in part by a recent publication by Ma et al. (2011) who resolved the asymptotic non-normality problem of the classical sample quantiles for discrete data through defining a new mid-distribution based quantile function. This work is the motivation for defining a new and improved smooth population quantile function given discrete data. Our definition is based on the theory of fractional order statistics. The main advantage of our definition as compared to its competitors is the capability to distinguish the u  th quantile across different discrete distributions over the whole interval, u∈(0,1)u∈(0,1). In addition, we define the corresponding estimator of the smooth population quantiles and demonstrate the convergence and asymptotic normal distribution of the corresponding sample quantiles. We verify our theoretical results through a Monte Carlo simulation, and illustrate the utilization of our quantile function in a Q–Q plot for discrete data.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 141, Issue 9, September 2011, Pages 3142–3150
نویسندگان
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