An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data

Adegoke Taiwo Mobolaji; Nicholas Pindar Dibal; Yahaya Abdullahi Musa

doi:doi:10.11648/j.ijdsa.20190501.11

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An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data

Adegoke Taiwo Mobolaji, Nicholas Pindar Dibal, Yahaya Abdullahi Musa

Published in International Journal of Data Science and Analysis (Volume 5, Issue 1)

Received: 26 December 2018 Accepted: 15 February 2019 Published: 28 March 2019

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Abstract

The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 1)
DOI	10.11648/j.ijdsa.20190501.11
Page(s)	1-5
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

Normal Distribution, Prior Distribution, Posterior Distribution, Bayesian Estimation, Inverse Gamma Distribution, Inverse Chi-Square Distribution, Levy Distribution, Gumbel Type II Distribution

References

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[5]	Fearnhead, P. and Prangle, D. (2012). Constructing Summary Statistics for Approximate Bayesian Computation: Semi-automatic ABC (with discussion). Journal of the Royal Statistical Society.
[6]	Kelvin P. Murphy (2017). Conjugate Bayesian analysis of the Gaussian distribution. Handbook on Bayesian Statistics, 1-29.
[7]	Marin, J., Pudlo, P., Robert, C. P. and Ryder, R. (2011). Approximate Bayesian Computational methods. Statistics and Computing.
[8]	Obisesan, K. (2015). Change-point detection in time series with hydrological applications. Master’s thesis, University College London.
[9]	Perreault, L., Bernier, J., Bobee B., Parent, E. (2000), Bayesian change-point analysis in hydro meteorological time series. Part 1. The normal model revisited. Journal of Hydrology 235, 221–241.
[10]	Pritchard, J. K., Seielstad, M. T., Perez-Lezaun, A., and Feldman, M. T. (1999). Population Growth of Human Y Chromosomes: A Study of Y. Chromosome Microsatellites. Molecular Biology and Evolution 16: 1791 1798.
[11]	Rebecca C. Steorts, (2016). Baby Bayes using R.
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[13]	Tendor Mihai Moldovan, (2010). The Conjugate Prior for the Normal Distribution, Technical report, 1-6.
[14]	Weisstein, E. W. (2012). Maximum Likelihood. From MathWorld—A Wolfram Web Resource. http://mathwor ld.wolfram.com/MaximumLikelihood.html.
[15]	Wilkinson, R. D. (2008). Approximate Bayesian computation (ABC) gives exact results under the assumption of error model. Arxiv preprint arXiv: 081 1.3355.
[16]	Yahya, W. B., Obisesan, K. O. and Adegoke, T. M. (2017), Bayesian Change-Point Modelling of Rainfall Distributions in Nigeria. Proceedings of 1^ST International Annual Conference of Nigeria Statistical Society, held at University of Ibadan Conference Center, Ibadan, Nigeria, 3RD to 5TH of April, 2017, 1, 59-63.

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APA Style

Adegoke Taiwo Mobolaji, Nicholas Pindar Dibal, Yahaya Abdullahi Musa. (2019). An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data. International Journal of Data Science and Analysis, 5(1), 1-5. https://doi.org/10.11648/j.ijdsa.20190501.11

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ACS Style

Adegoke Taiwo Mobolaji; Nicholas Pindar Dibal; Yahaya Abdullahi Musa. An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data. Int. J. Data Sci. Anal. 2019, 5(1), 1-5. doi: 10.11648/j.ijdsa.20190501.11

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AMA Style

Adegoke Taiwo Mobolaji, Nicholas Pindar Dibal, Yahaya Abdullahi Musa. An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data. Int J Data Sci Anal. 2019;5(1):1-5. doi: 10.11648/j.ijdsa.20190501.11

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@article{10.11648/j.ijdsa.20190501.11,
  author = {Adegoke Taiwo Mobolaji and Nicholas Pindar Dibal and Yahaya Abdullahi Musa},
  title = {An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ijdsa.20190501.11},
  url = {https://doi.org/10.11648/j.ijdsa.20190501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190501.11},
  abstract = {The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.},
 year = {2019}
}

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TY  - JOUR
T1  - An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data
AU  - Adegoke Taiwo Mobolaji
AU  - Nicholas Pindar Dibal
AU  - Yahaya Abdullahi Musa
Y1  - 2019/03/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190501.11
DO  - 10.11648/j.ijdsa.20190501.11
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  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190501.11
AB  - The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.
VL  - 5
IS  - 1
ER  -

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Author Information

Adegoke Taiwo Mobolaji

Department of Statistics, University of Ilorin, Ilorin, Nigeria
Nicholas Pindar Dibal

Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria
Yahaya Abdullahi Musa

Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria

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APA Style

Adegoke Taiwo Mobolaji, Nicholas Pindar Dibal, Yahaya Abdullahi Musa. (2019). An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data. International Journal of Data Science and Analysis, 5(1), 1-5. https://doi.org/10.11648/j.ijdsa.20190501.11

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ACS Style

Adegoke Taiwo Mobolaji; Nicholas Pindar Dibal; Yahaya Abdullahi Musa. An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data. Int. J. Data Sci. Anal. 2019, 5(1), 1-5. doi: 10.11648/j.ijdsa.20190501.11

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AMA Style

Adegoke Taiwo Mobolaji, Nicholas Pindar Dibal, Yahaya Abdullahi Musa. An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data. Int J Data Sci Anal. 2019;5(1):1-5. doi: 10.11648/j.ijdsa.20190501.11

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@article{10.11648/j.ijdsa.20190501.11,
  author = {Adegoke Taiwo Mobolaji and Nicholas Pindar Dibal and Yahaya Abdullahi Musa},
  title = {An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ijdsa.20190501.11},
  url = {https://doi.org/10.11648/j.ijdsa.20190501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190501.11},
  abstract = {The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.},
 year = {2019}
}

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TY  - JOUR
T1  - An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data
AU  - Adegoke Taiwo Mobolaji
AU  - Nicholas Pindar Dibal
AU  - Yahaya Abdullahi Musa
Y1  - 2019/03/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190501.11
DO  - 10.11648/j.ijdsa.20190501.11
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  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190501.11
AB  - The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.
VL  - 5
IS  - 1
ER  -

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