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), 2020. Published by Science Publishing Group

Keywords

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

References

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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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