Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya

Stella Mutahi; Thomas Mageto; Antony Ngunyi

doi:doi:10.11648/j.ijdsa.20200606.15

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Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya

Stella Mutahi, Thomas Mageto, Antony Ngunyi

Published in International Journal of Data Science and Analysis (Volume 6, Issue 6)

Received: 3 December 2020 Accepted: 10 December 2020 Published: 22 December 2020

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Abstract

Mathematical literacy is the ability to use numbers to help solve real-world problems. It focuses on pupils' ability to analyze, justify and communicate ideas effectively with regard to formulating, solving and interpreting Mathematical problems in a variety of forms and situations. The study modeled above threshold scores in mathematics among school pupils as an indicator for being mathematically literate. Modeling was on the inter-arrival times for pupils scoring above threshold scores (Mathematics mean score) for a given sample of pupils in their mid and end of term examinations. The Poisson distribution has been widely used as a statistical procedure for modeling inter-arrival times for count data outcomes. However, for heavy-tailed inter-arrival times of successive outcomes, the Poisson distribution exhibits an empirical observational failure thus setting up a framework for the use of other distributions that can handle such heavy-tailed data. The study used the generalized Gumbel and Weibull inter-arrival time distributions which were assumed to nest the standard Poisson distribution in which Weibull inter-arrival gave a better fit to the data. Data used was secondary data on pupil performance in Mathematics in relation to other subjects from Acacia Crest School.

Published in	International Journal of Data Science and Analysis (Volume 6, Issue 6)
DOI	10.11648/j.ijdsa.20200606.15
Page(s)	213-219
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), 2024. Published by Science Publishing Group

Keywords

Threshold Scores, Inter-Arrival Times, Gumbel and Weibull Distributions

References

[1]	Dokter, A. M, Emiel, E., Wimke, F., Lameris, T. K., Bart, A. N. & Henk, P. (2017). Analyzing time-ordered event data with missed observations. Ecology and Evolution. 2017 (7); 7362–7369. doi: 10.1002/ece3.3281.
[2]	Sahana, B. (2018). A Counting Process with Generalized Exponential Inter-Arrival Times. Statistica, 2018 (1).
[3]	Bushra, M. A., Abdalla, M. H., Mohammed, S. M., Bassi, J. S., Ismahani, I. & Muhammad, N. M. (2018). Impact of Packet Inter-arrival Time Features for Online Peer-to-Peer (P2P) Classification. International Journal of Electrical and Computer Engineering (.ECE), 8 (4); 2521-2530. doi: 10.11591/¼ece. V8i4. Pp 2521-2530.
[4]	Farayibi, A. (2016). Investigating the Application of Queue Theory in the Nigerian Banking System. Centre for Allied Research and Economic Development, Ibadan, Oyo State, Nigeria. MPRA Paper No. 73614, posted 12 Sep 2016 08: 24 UTC. https://mpra.ub.unimuenchen.
[5]	Harahap, E. (2019). Modeling and simulation of queue waiting time at traffic light intersection. Journal of Physics: Conference Series. IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012001 IOP Publishing doi: 10.1088/1742-6596/1188/1/012001.39.
[6]	Alexei, V., João, G., Zoltán, D., Kwang-Il, G., Imre, K. & Barabási, A. L. (2006). Modelingbursts and heavy tails in human dynamics. Physical Review E 73, 036127 (2006). DOI: 10.1103/PhysRevE.73.036127.
[7]	Gleb, Y., Rundle, J. B., Shcherbakov, R. & Turcottet, D. L. (2008). Inter-arrival time distributionfor the non-homogeneous Poisson process. arXiv: cond-mat/0507657v1 [condmat. stat- mech] 27 Jul 2005.
[8]	Seigha, G., Gordon, M. B. & Mobolaji, H. O. (2016). Application of Queuing Theory to a Fast Food Outfit; A study of Blue Meadows Restaurant. Independent Journal of Management & Production, 8 (2); April - June 2017. ISSN: 2236-269X DOI: 10.14807/¼mp.v8i2.576.
[9]	Mohammad, S. R. C., Mohammad, T. R. & Mohammad, R. K. (2013). Solving Of Waiting Lines Models in the Bank Using Queuing Theory Model the Practice Case: Islami Bank Bangladesh Limited, Chawkbazar Branch and Chittagong. IOSR Journal of Business and Management (IOSR-JBM), 10 (1); 22-29. www.iosrjournals.org.
[10]	Onoja, A. & Kembe, M. (2018). The Application of Queuing Theory on Patient Waiting Time in Ante-natal Care Clinic. International Journal of Science and Technology. January 2018.
[11]	Cameron, A. C. & Johansson, P. (1997). Count Data Regression Using Series Expansion: With Applications. Journal of Applied Econometrics, 12; 203-223.
[12]	Mcshane, B., Adrian, M., Bradlow, E. T. & Fader, P. S. (2008). Count models based on Weibull inter-arrival times. Journal of Business and Economic Statistics, 26 (3), 369-378.
[13]	Cox, D. R. (1972). Regression Models and Life-Tables. Journal of the Royal Statistical Society, Ser. B, 34, 187–220.
[14]	Thiagarajan, M. & Andrew, A. M. (2020). Queuing Theory Based on Decentralized Onload Data Arrival Using Expected Max-Min Probabilistic Decision for Reducing Workload. Journal of Critical Reviews, 7 (6); 107-110. doi: 10.31838/jcr.07.06.21.
[15]	Manu, L., Dries, F. B. & Develder, C. (2020). Synthetic Data Generator for Electric Vehicle Charging Sessions; Modeling and Evaluation Using Real-World Data. Energies 2020, 13 (4211); 1-18. doi: 10.3390/en13164211.
[16]	Stoynov, P., Zlatera, P. & Velev, D. (2015). An Approach for Modeling Inter-Arrival Time of Floods. International Journal of Innovation, Management and Technology, 6 (4); 267-271. doi: 10.7763/¼imt.2015.v6.613.
[17]	Eri, I. & Mihaela, M. (2019). Queue-Based Modeling of the Aircraft Arrival Process at a Single Airport. Aerospace 2019, 6 (103); 1-20. doi: 3390/aerospace6100103.

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APA Style

Stella Mutahi, Thomas Mageto, Antony Ngunyi. (2020). Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya. International Journal of Data Science and Analysis, 6(6), 213-219. https://doi.org/10.11648/j.ijdsa.20200606.15

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ACS Style

Stella Mutahi; Thomas Mageto; Antony Ngunyi. Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya. Int. J. Data Sci. Anal. 2020, 6(6), 213-219. doi: 10.11648/j.ijdsa.20200606.15

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AMA Style

Stella Mutahi, Thomas Mageto, Antony Ngunyi. Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya. Int J Data Sci Anal. 2020;6(6):213-219. doi: 10.11648/j.ijdsa.20200606.15

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@article{10.11648/j.ijdsa.20200606.15,
  author = {Stella Mutahi and Thomas Mageto and Antony Ngunyi},
  title = {Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {6},
  pages = {213-219},
  doi = {10.11648/j.ijdsa.20200606.15},
  url = {https://doi.org/10.11648/j.ijdsa.20200606.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200606.15},
  abstract = {Mathematical literacy is the ability to use numbers to help solve real-world problems. It focuses on pupils' ability to analyze, justify and communicate ideas effectively with regard to formulating, solving and interpreting Mathematical problems in a variety of forms and situations. The study modeled above threshold scores in mathematics among school pupils as an indicator for being mathematically literate. Modeling was on the inter-arrival times for pupils scoring above threshold scores (Mathematics mean score) for a given sample of pupils in their mid and end of term examinations. The Poisson distribution has been widely used as a statistical procedure for modeling inter-arrival times for count data outcomes. However, for heavy-tailed inter-arrival times of successive outcomes, the Poisson distribution exhibits an empirical observational failure thus setting up a framework for the use of other distributions that can handle such heavy-tailed data. The study used the generalized Gumbel and Weibull inter-arrival time distributions which were assumed to nest the standard Poisson distribution in which Weibull inter-arrival gave a better fit to the data. Data used was secondary data on pupil performance in Mathematics in relation to other subjects from Acacia Crest School.},
 year = {2020}
}

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TY  - JOUR
T1  - Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya
AU  - Stella Mutahi
AU  - Thomas Mageto
AU  - Antony Ngunyi
Y1  - 2020/12/22
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdsa.20200606.15
DO  - 10.11648/j.ijdsa.20200606.15
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 213
EP  - 219
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20200606.15
AB  - Mathematical literacy is the ability to use numbers to help solve real-world problems. It focuses on pupils' ability to analyze, justify and communicate ideas effectively with regard to formulating, solving and interpreting Mathematical problems in a variety of forms and situations. The study modeled above threshold scores in mathematics among school pupils as an indicator for being mathematically literate. Modeling was on the inter-arrival times for pupils scoring above threshold scores (Mathematics mean score) for a given sample of pupils in their mid and end of term examinations. The Poisson distribution has been widely used as a statistical procedure for modeling inter-arrival times for count data outcomes. However, for heavy-tailed inter-arrival times of successive outcomes, the Poisson distribution exhibits an empirical observational failure thus setting up a framework for the use of other distributions that can handle such heavy-tailed data. The study used the generalized Gumbel and Weibull inter-arrival time distributions which were assumed to nest the standard Poisson distribution in which Weibull inter-arrival gave a better fit to the data. Data used was secondary data on pupil performance in Mathematics in relation to other subjects from Acacia Crest School.
VL  - 6
IS  - 6
ER  -

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Author Information

Stella Mutahi

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Thomas Mageto

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Antony Ngunyi

Department of Statistics and Actuarial Science, Dedan Kimathi University of Technology, Nyeri, Kenya

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APA Style

Stella Mutahi, Thomas Mageto, Antony Ngunyi. (2020). Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya. International Journal of Data Science and Analysis, 6(6), 213-219. https://doi.org/10.11648/j.ijdsa.20200606.15

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ACS Style

Stella Mutahi; Thomas Mageto; Antony Ngunyi. Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya. Int. J. Data Sci. Anal. 2020, 6(6), 213-219. doi: 10.11648/j.ijdsa.20200606.15

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AMA Style

Stella Mutahi, Thomas Mageto, Antony Ngunyi. Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya. Int J Data Sci Anal. 2020;6(6):213-219. doi: 10.11648/j.ijdsa.20200606.15

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@article{10.11648/j.ijdsa.20200606.15,
  author = {Stella Mutahi and Thomas Mageto and Antony Ngunyi},
  title = {Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {6},
  pages = {213-219},
  doi = {10.11648/j.ijdsa.20200606.15},
  url = {https://doi.org/10.11648/j.ijdsa.20200606.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200606.15},
  abstract = {Mathematical literacy is the ability to use numbers to help solve real-world problems. It focuses on pupils' ability to analyze, justify and communicate ideas effectively with regard to formulating, solving and interpreting Mathematical problems in a variety of forms and situations. The study modeled above threshold scores in mathematics among school pupils as an indicator for being mathematically literate. Modeling was on the inter-arrival times for pupils scoring above threshold scores (Mathematics mean score) for a given sample of pupils in their mid and end of term examinations. The Poisson distribution has been widely used as a statistical procedure for modeling inter-arrival times for count data outcomes. However, for heavy-tailed inter-arrival times of successive outcomes, the Poisson distribution exhibits an empirical observational failure thus setting up a framework for the use of other distributions that can handle such heavy-tailed data. The study used the generalized Gumbel and Weibull inter-arrival time distributions which were assumed to nest the standard Poisson distribution in which Weibull inter-arrival gave a better fit to the data. Data used was secondary data on pupil performance in Mathematics in relation to other subjects from Acacia Crest School.},
 year = {2020}
}

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TY  - JOUR
T1  - Inter-Arrival Time Modeling of Threshold Scores in Mathematics Among School Pupils; A Case of Acacia Crest School, Kenya
AU  - Stella Mutahi
AU  - Thomas Mageto
AU  - Antony Ngunyi
Y1  - 2020/12/22
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdsa.20200606.15
DO  - 10.11648/j.ijdsa.20200606.15
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 213
EP  - 219
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20200606.15
AB  - Mathematical literacy is the ability to use numbers to help solve real-world problems. It focuses on pupils' ability to analyze, justify and communicate ideas effectively with regard to formulating, solving and interpreting Mathematical problems in a variety of forms and situations. The study modeled above threshold scores in mathematics among school pupils as an indicator for being mathematically literate. Modeling was on the inter-arrival times for pupils scoring above threshold scores (Mathematics mean score) for a given sample of pupils in their mid and end of term examinations. The Poisson distribution has been widely used as a statistical procedure for modeling inter-arrival times for count data outcomes. However, for heavy-tailed inter-arrival times of successive outcomes, the Poisson distribution exhibits an empirical observational failure thus setting up a framework for the use of other distributions that can handle such heavy-tailed data. The study used the generalized Gumbel and Weibull inter-arrival time distributions which were assumed to nest the standard Poisson distribution in which Weibull inter-arrival gave a better fit to the data. Data used was secondary data on pupil performance in Mathematics in relation to other subjects from Acacia Crest School.
VL  - 6
IS  - 6
ER  -

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