Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production

Abubakar Usman Yusuf; Lawal Adamu; Muhammed Abdullahi

doi:doi:10.11648/j.ajtas.20140302.12

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Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production

Abubakar Usman Yusuf, Lawal Adamu, Muhammed Abdullahi

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 2)

Received: 30 December 2013 Published: 20 March 2014

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Abstract

A stochastic process with a first order dependence in discrete state and time is described as Markov chain. This principle was used to formulate a four state model for annual rainfall distribution in Minna with respect to crop production. The model is designed such that if given any of the four state in a given year, it is possible to determine quantitatively the probability of making transition to any other three states in the following year(s) and in the long-run. The model was used to study the data of annual rainfall in Minna. The results show that in the long run 14% of annual rainfall shall be low rainfall, 34% annual rainfall will be moderate rainfall also well spread, 47% of the annual rainfall shall be high rainfall and 5% of the annual rainfall shall be moderate rainfall not well spread respectively. The model provides some information about rainfall in relation to crops cultivation that could be used by the farmers and the government to plan strategy for high crop production in Minna and the immediate environment.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 2)
DOI	10.11648/j.ajtas.20140302.12
Page(s)	39-43
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), 2014. Published by Science Publishing Group

Keywords

Markov Chain, Rainfall, Crop Production, Transition Probability

References

[1]	Akintunde A.A, Asiribo O.E. Adebanji A.O. Adelakun A.A Agwuegbo S.O.N. (2008) Stochastic modelling of daily precipitation in Abeokuta, proceedings of the third Confersence on science and National Development pp108-118 www.unaab.edu.ng/journal/index.php/COLNAS/article/.../150/153. Accessed 15/10/2012.
[2]	Gabriel, K. R. and Neumann, J. (1962) A Markov chain model for daily rainfall occurrences at Tel Aviv. Quart. J. Roy. Met. Soc. 88:90-95.
[3]	Jain S. (1986), A Markov Chain Model and its Application, Comp.Biomed. Res. 19. 374-378
[4]	Jimoh, O. D. and Webster, P. (1996). Optimum order of Markov chain for daily rainfall in Nigeria. Journal of Hydrology 185: 45-69.
[5]	Jimoh, O. D. and Webster, P. (1999). Stochastic modelling daily rainfall in Nigeria: intra-annual variation of model parameters. Journal of Hydrology 222:1- 17.
[6]	Kottegoda, N. T., Natale, L. and Raiteri, E. (2004); Some considerations of periodicity and persistence in daily rainfalls, J. Hydrol. 296:23–37.
[7]	Cox D.R., and Miller H.D. (1984). The Theory of Stochastic Processes. Chapman and Hall London.
[8]	NMAM (2011), Unpublished records of the Nigerian Meteorological Service Department, Federal Ministry of Aviation Minna.
[9]	NSADP (2011). Unpublished document of the Niger State Agricultural Development Project. A Department in the ministry of Agriculture and Rural development.
[10]	Howard R.A.(1971), Dynamic Probabilistic Systems, Vols.1and2. John Wiley, New York.
[11]	Iloeje N.P. (1981), A New Goegraphy of Nigeria, Longman Nigeria Limited.
[12]	Ross S.M. (1989), Introduction to Probability Models Academic Press, Inc. Ltd , London.
[13]	Abubakar U.Y., Lawal A., Muhammed A. (2013). The Use of Markov Model in Continuous Time for the Prediction of Rainfall for Crop Production, International Organization for Scientific Research, (IOSR) Vol.7, Issue1, pp 38 – 45.

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APA Style

Abubakar Usman Yusuf, Lawal Adamu, Muhammed Abdullahi. (2014). Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production. American Journal of Theoretical and Applied Statistics, 3(2), 39-43. https://doi.org/10.11648/j.ajtas.20140302.12

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ACS Style

Abubakar Usman Yusuf; Lawal Adamu; Muhammed Abdullahi. Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production. Am. J. Theor. Appl. Stat. 2014, 3(2), 39-43. doi: 10.11648/j.ajtas.20140302.12

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AMA Style

Abubakar Usman Yusuf, Lawal Adamu, Muhammed Abdullahi. Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production. Am J Theor Appl Stat. 2014;3(2):39-43. doi: 10.11648/j.ajtas.20140302.12

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@article{10.11648/j.ajtas.20140302.12,
  author = {Abubakar Usman Yusuf and Lawal Adamu and Muhammed Abdullahi},
  title = {Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {2},
  pages = {39-43},
  doi = {10.11648/j.ajtas.20140302.12},
  url = {https://doi.org/10.11648/j.ajtas.20140302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140302.12},
  abstract = {A stochastic process with a first order dependence in discrete state and time is described as Markov chain. This principle was used to formulate a four state model for annual rainfall distribution in Minna with respect to crop production. The model is designed such that if given any of the four state in a given year, it is possible to determine quantitatively the probability of making transition to any other three states in the following year(s) and in the long-run. The model was used to study the data of annual rainfall in Minna. The results show that in the long run 14% of annual rainfall shall be low rainfall, 34% annual rainfall will be moderate rainfall also well spread, 47% of the annual rainfall shall be high rainfall and 5% of the annual rainfall shall be moderate rainfall not well spread respectively. The model provides some information about rainfall in relation to crops cultivation that could be used by the farmers and the government to plan strategy for high crop production in Minna and the immediate environment.},
 year = {2014}
}

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TY  - JOUR
T1  - Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production
AU  - Abubakar Usman Yusuf
AU  - Lawal Adamu
AU  - Muhammed Abdullahi
Y1  - 2014/03/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140302.12
DO  - 10.11648/j.ajtas.20140302.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 39
EP  - 43
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140302.12
AB  - A stochastic process with a first order dependence in discrete state and time is described as Markov chain. This principle was used to formulate a four state model for annual rainfall distribution in Minna with respect to crop production. The model is designed such that if given any of the four state in a given year, it is possible to determine quantitatively the probability of making transition to any other three states in the following year(s) and in the long-run. The model was used to study the data of annual rainfall in Minna. The results show that in the long run 14% of annual rainfall shall be low rainfall, 34% annual rainfall will be moderate rainfall also well spread, 47% of the annual rainfall shall be high rainfall and 5% of the annual rainfall shall be moderate rainfall not well spread respectively. The model provides some information about rainfall in relation to crops cultivation that could be used by the farmers and the government to plan strategy for high crop production in Minna and the immediate environment.
VL  - 3
IS  - 2
ER  -

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Author Information

Abubakar Usman Yusuf

Department of Mathematics and Statistics, Federal University of Technology, Minna, Nigeria
Lawal Adamu

Department of Mathematics and Statistics, Federal University of Technology, Minna, Nigeria
Muhammed Abdullahi

Department of Mathematics and Statistics, Federal University of Technology, Minna, Nigeria

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APA Style

Abubakar Usman Yusuf, Lawal Adamu, Muhammed Abdullahi. (2014). Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production. American Journal of Theoretical and Applied Statistics, 3(2), 39-43. https://doi.org/10.11648/j.ajtas.20140302.12

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ACS Style

Abubakar Usman Yusuf; Lawal Adamu; Muhammed Abdullahi. Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production. Am. J. Theor. Appl. Stat. 2014, 3(2), 39-43. doi: 10.11648/j.ajtas.20140302.12

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AMA Style

Abubakar Usman Yusuf, Lawal Adamu, Muhammed Abdullahi. Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production. Am J Theor Appl Stat. 2014;3(2):39-43. doi: 10.11648/j.ajtas.20140302.12

Copy | Download

@article{10.11648/j.ajtas.20140302.12,
  author = {Abubakar Usman Yusuf and Lawal Adamu and Muhammed Abdullahi},
  title = {Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {2},
  pages = {39-43},
  doi = {10.11648/j.ajtas.20140302.12},
  url = {https://doi.org/10.11648/j.ajtas.20140302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140302.12},
  abstract = {A stochastic process with a first order dependence in discrete state and time is described as Markov chain. This principle was used to formulate a four state model for annual rainfall distribution in Minna with respect to crop production. The model is designed such that if given any of the four state in a given year, it is possible to determine quantitatively the probability of making transition to any other three states in the following year(s) and in the long-run. The model was used to study the data of annual rainfall in Minna. The results show that in the long run 14% of annual rainfall shall be low rainfall, 34% annual rainfall will be moderate rainfall also well spread, 47% of the annual rainfall shall be high rainfall and 5% of the annual rainfall shall be moderate rainfall not well spread respectively. The model provides some information about rainfall in relation to crops cultivation that could be used by the farmers and the government to plan strategy for high crop production in Minna and the immediate environment.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Markov Chain Model and Its Application to Annual Rainfall Distribution for Crop Production
AU  - Abubakar Usman Yusuf
AU  - Lawal Adamu
AU  - Muhammed Abdullahi
Y1  - 2014/03/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140302.12
DO  - 10.11648/j.ajtas.20140302.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 39
EP  - 43
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140302.12
AB  - A stochastic process with a first order dependence in discrete state and time is described as Markov chain. This principle was used to formulate a four state model for annual rainfall distribution in Minna with respect to crop production. The model is designed such that if given any of the four state in a given year, it is possible to determine quantitatively the probability of making transition to any other three states in the following year(s) and in the long-run. The model was used to study the data of annual rainfall in Minna. The results show that in the long run 14% of annual rainfall shall be low rainfall, 34% annual rainfall will be moderate rainfall also well spread, 47% of the annual rainfall shall be high rainfall and 5% of the annual rainfall shall be moderate rainfall not well spread respectively. The model provides some information about rainfall in relation to crops cultivation that could be used by the farmers and the government to plan strategy for high crop production in Minna and the immediate environment.
VL  - 3
IS  - 2
ER  -

Copy | Download