This paper is twofold. On the one hand, standpipe water data for small rural communities in Meknes region are studied. 89 villages with population less than 1200 have been probed. In total, about 37000 inhabitants are covered by this study. From the conducted analysis, it appears that the daily per capita water-use rate for the considered population is uniformly distributed with an estimated average of about 10 liter. The lower and the upper 95% confidence bounds placed on this average are 4.3 and 15.9; respectively. Such data can, for example, be useful while planning regional water conveyance systems. On the other hand, the statistical test used in this work is based on the closed form of the Shapiro-Wilk statistic, Wu, made explicit by Cheng and Spiring in the case of uniformly distributed random variables. Even though Wu is computationally simple, its sampling distribution seems to be intractable for arbitrarily sample-size values. On that account, Monte Carlo simulations are run to generate custom quantiles frequently needed in a typical hypothesis testing problem. Then, the study extends and improves the Cheng-Spiring quantile Table 1 for testing for the uniform distribution. It also proposes a simplified and user-friendly graphical support which serves the same task.
| Published in | Earth Sciences (Volume 12, Issue 3) |
| DOI | 10.11648/j.earth.20231203.12 |
| Page(s) | 65-73 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2023. Published by Science Publishing Group |
Water-Use, Standpipe, Rural, Uniform Distribution, Shapiro-Wilk Statistic, Méknes, INDH
| [1] | Troin, J.-F. (2002). Maroc, Régions, pays, territoires. 1st Ed. Maisonneuve & Larose, Paris. ISBN: 2-7068-1630-9, pp: 502. |
| [2] | Draper, N. R., & Smith, H. (1998). Applied Regression Analysis. New York. John Wiley & Sons, 3rd Ed. ISBN: 0-471-17082-8, pp: 705. |
| [3] | Maddala, G. S. (1992). Introduction to Econometrics. New York. Macmillan, 2nd Ed. ISBN: 0-02-374545-2, pp: 637. |
| [4] | Lloyd, E. H. (1952). Least squares estimation of location and scale parameters using order statistics, Biometrika, 39: 88-95. DOI: 10.2307/2332466. |
| [5] | Wainwright, M. J. (2019). High-Dimensional Statistics, a Non-Asymptotic Viewpoint. Cambridge. Cambridge University Press, 1st Ed. ISBN: 978-1-108-49802-9, pp: 572. |
| [6] | Cox, D. R. & Hinkley, D. V. (1974). Theoretical Statistics. London. Chapman and Hall, 1st Ed. ISBN: 978-0-412-12420-4, pp: 522. |
| [7] | Emmert-Streib, F. & Dehmer, M. (2019). Understanding statistical hypothesis testing: The logic of statistical inference. Machine Learning & knowledge Extraction, 1, pp 945-961, DOI: 10.3390/make1030054. |
| [8] | Cheng, S. W. & Spiring. F. A. (1987). A test to identify the uniform distribution, with applications to probability plotting and other distributions. IEEE Transactions on Reliability, R-36 (1): 98-105. DOI: 10.1016/0026-2714(88)90079-0. |
| [9] | Goodman, J. (1983). Accuracy and efficiency of Monte Carlo method. Bechtel Power Corporation, 12400, E. Imperial Hwy. Norwalk, CA 90650, USA. (online paper) https://inis.iaea.org>-publication |
| [10] | Rubinstein, R. Y. & Kroese, D. P. (2017). Simulation and Monte Carlo Method. Hoboken. John Wiley & Sons, 3rd Ed. ISBN: 9781118632208, pp: 396. |
| [11] | Becker, R. A. & Chambers, J. M. (1984). S: An Interactive Environment for Data Analysis and Graphics. Belmont California. Chapman and Hall, 1st Ed. ISBN 10: 0-534-03313-X, pp: 580. |
| [12] | Avramidis, A. N. & Wilson. J. R. (1998). Correlation-induction techniques for estimating quantiles in simulation experiments. Operation Research, 46 (4): 574-591. DOI: 10.1145/224401.224614. |
| [13] | Miller, R. G. (1974). The jackknife – A review. Biometrika, 61 (1): 1-15. JSTOR, DOI: 10.2307/2334280. |
| [14] | Ioannidis, J. P. A. (2005). Why most published research findings are false, PLoS Medicine, 2 (8) e124: 696-701. DOI: 101371/journal.pmed.0010124. |
| [15] | Casella, G. & Berger, R. L. (2002), Statistical Inference. United States, Duxbury, 2nd Ed. ISBN-13: 978-0534243128, pp 498. |
| [16] | Hastie, T., Tibshirani, R. & Friedman, J. (2009). The Elements of Statistical Learning. New York. Springer, 2nd Ed. ISBN-13: 978-0387848570, pp: 764. |
| [17] | Gradshteyn, I. S., & Ryzhik, I. M. (2007). Tables of Integrals, Series and Products. San Diego. Elsevier, 7th Ed. ISBN-13: 978-0-12-373637-6, pp: 1220. |
| [18] | Bolashvili, N., Karalashvili, T., Geladze, V., Machavariani, N., Karalashvili, A., Chikhradze, N., Giorgi, G. & Kartvelishvili. (2017). Sustainable management of water resources on the background of current climate change. Earth Sciences. Vol. 6. No. 5. pp 75-79. DOI. 10.11648/j.earth.20170605.13. |
APA Style
Mohamed Saffi. (2023). Summarizing Standpipe Water Data for Meknes Small Rural Communities (Morocco): An Extended Table for Testing for the Uniform Distribution. Earth Sciences, 12(3), 65-73. https://doi.org/10.11648/j.earth.20231203.12
ACS Style
Mohamed Saffi. Summarizing Standpipe Water Data for Meknes Small Rural Communities (Morocco): An Extended Table for Testing for the Uniform Distribution. Earth Sci. 2023, 12(3), 65-73. doi: 10.11648/j.earth.20231203.12
AMA Style
Mohamed Saffi. Summarizing Standpipe Water Data for Meknes Small Rural Communities (Morocco): An Extended Table for Testing for the Uniform Distribution. Earth Sci. 2023;12(3):65-73. doi: 10.11648/j.earth.20231203.12
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Download@article{10.11648/j.earth.20231203.12,
author = {Mohamed Saffi},
title = {Summarizing Standpipe Water Data for Meknes Small Rural Communities (Morocco): An Extended Table for Testing for the Uniform Distribution},
journal = {Earth Sciences},
volume = {12},
number = {3},
pages = {65-73},
doi = {10.11648/j.earth.20231203.12},
url = {https://doi.org/10.11648/j.earth.20231203.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20231203.12},
abstract = {This paper is twofold. On the one hand, standpipe water data for small rural communities in Meknes region are studied. 89 villages with population less than 1200 have been probed. In total, about 37000 inhabitants are covered by this study. From the conducted analysis, it appears that the daily per capita water-use rate for the considered population is uniformly distributed with an estimated average of about 10 liter. The lower and the upper 95% confidence bounds placed on this average are 4.3 and 15.9; respectively. Such data can, for example, be useful while planning regional water conveyance systems. On the other hand, the statistical test used in this work is based on the closed form of the Shapiro-Wilk statistic, Wu, made explicit by Cheng and Spiring in the case of uniformly distributed random variables. Even though Wu is computationally simple, its sampling distribution seems to be intractable for arbitrarily sample-size values. On that account, Monte Carlo simulations are run to generate custom quantiles frequently needed in a typical hypothesis testing problem. Then, the study extends and improves the Cheng-Spiring quantile Table 1 for testing for the uniform distribution. It also proposes a simplified and user-friendly graphical support which serves the same task.},
year = {2023}
}
TY - JOUR T1 - Summarizing Standpipe Water Data for Meknes Small Rural Communities (Morocco): An Extended Table for Testing for the Uniform Distribution AU - Mohamed Saffi Y1 - 2023/06/20 PY - 2023 N1 - https://doi.org/10.11648/j.earth.20231203.12 DO - 10.11648/j.earth.20231203.12 T2 - Earth Sciences JF - Earth Sciences JO - Earth Sciences SP - 65 EP - 73 PB - Science Publishing Group SN - 2328-5982 UR - https://doi.org/10.11648/j.earth.20231203.12 AB - This paper is twofold. On the one hand, standpipe water data for small rural communities in Meknes region are studied. 89 villages with population less than 1200 have been probed. In total, about 37000 inhabitants are covered by this study. From the conducted analysis, it appears that the daily per capita water-use rate for the considered population is uniformly distributed with an estimated average of about 10 liter. The lower and the upper 95% confidence bounds placed on this average are 4.3 and 15.9; respectively. Such data can, for example, be useful while planning regional water conveyance systems. On the other hand, the statistical test used in this work is based on the closed form of the Shapiro-Wilk statistic, Wu, made explicit by Cheng and Spiring in the case of uniformly distributed random variables. Even though Wu is computationally simple, its sampling distribution seems to be intractable for arbitrarily sample-size values. On that account, Monte Carlo simulations are run to generate custom quantiles frequently needed in a typical hypothesis testing problem. Then, the study extends and improves the Cheng-Spiring quantile Table 1 for testing for the uniform distribution. It also proposes a simplified and user-friendly graphical support which serves the same task. VL - 12 IS - 3 ER -
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