Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster a quick and a deep understanding of the data as an important basis for successful data analytics. Furthermore, new...
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Instituto Nacional de Estatística | Statistics Portugal
2025-02-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/438 |
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| author | Elsayed A. H. Elamir |
| author_facet | Elsayed A. H. Elamir |
| author_sort | Elsayed A. H. Elamir |
| collection | DOAJ |
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Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster a quick and a deep understanding of the data as an important basis for successful data analytics. Furthermore, new nonparametric approaches for estimating the cumulative distribution function based on the mean absolute deviation function are proposed. These new approaches are meant to be a general nonparametric class that includes the empirical distribution function as a special case. Simulation study reveals that the Richardson extrapolation approach has a major improvement in terms of average squared errors over the classical empirical estimators and has comparable results with smooth approaches such as cubic spline and constrained linear spline for practically small samples. The properties of the proposed estimators are studied. Moreover, the Richardson approach has been applied to real data analysis and has been used to estimate the hazardous concentration five percent.
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| format | Article |
| id | doaj-art-57d0a690990e4e0eb9c891c39016738d |
| institution | Kabale University |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-57d0a690990e4e0eb9c891c39016738d2025-02-06T10:52:05ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-02-0123110.57805/revstat.v23i1.438Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric ApproachElsayed A. H. Elamir0University of Bahrain Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster a quick and a deep understanding of the data as an important basis for successful data analytics. Furthermore, new nonparametric approaches for estimating the cumulative distribution function based on the mean absolute deviation function are proposed. These new approaches are meant to be a general nonparametric class that includes the empirical distribution function as a special case. Simulation study reveals that the Richardson extrapolation approach has a major improvement in terms of average squared errors over the classical empirical estimators and has comparable results with smooth approaches such as cubic spline and constrained linear spline for practically small samples. The properties of the proposed estimators are studied. Moreover, the Richardson approach has been applied to real data analysis and has been used to estimate the hazardous concentration five percent. https://revstat.ine.pt/index.php/REVSTAT/article/view/438empirical distribution functionnonparametric estimationnumerical differentiationRichardson extrapolationskewnessuniform consistency |
| spellingShingle | Elsayed A. H. Elamir Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach Revstat Statistical Journal empirical distribution function nonparametric estimation numerical differentiation Richardson extrapolation skewness uniform consistency |
| title | Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach |
| title_full | Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach |
| title_fullStr | Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach |
| title_full_unstemmed | Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach |
| title_short | Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach |
| title_sort | data analytics and distribution function estimation via mean absolute deviation nonparametric approach |
| topic | empirical distribution function nonparametric estimation numerical differentiation Richardson extrapolation skewness uniform consistency |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/438 |
| work_keys_str_mv | AT elsayedahelamir dataanalyticsanddistributionfunctionestimationviameanabsolutedeviationnonparametricapproach |