On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria

Kazeem Olalekan Obisesan; Oladapo Muyiwa Oladoja

doi:doi:10.11648/j.ijsd.20220802.11

| Peer-Reviewed

On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria

Kazeem Olalekan Obisesan, Oladapo Muyiwa Oladoja

Published in International Journal of Statistical Distributions and Applications (Volume 8, Issue 2)

Received: 6 April 2022 Accepted: 19 April 2022 Published: 10 May 2022

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Normal processes produce random variables with a normal distribution, which is the most important model in statistics. Due to the constant speed and direction of the carrier medium, a continuous source releases particles like environmental pollutants in drift be it in the air, water or soil. By differentiating the normal density function, this study used the knowledge of the plume model to build two separate paths of utilizing Gaussian probability density function with mean of zero to show that it meets the diffusion equation from physical principles through the knowledge of a Brownian motion in monitoring emissions of carbon monoxide from different sources in the most populous black country. Carbon monoxide emissions from manufacturing industries and construction (MIC), fugitive emissions from solid fuels (FESO), and agricultural waste burning (AWB) are all higher than other sources in Nigeria, according to this research. Rail transportation (RAIL) is the lowest source of carbon monoxide emissions, and pollution diffusion in the country follows a predictable pattern in form of a normal process. The magnitude of the standard deviations affects the precision of confidence intervals used to estimate mean pollutant concentrations. Decision-makers in the country will know which sectors to focus on in order to reduce carbon monoxide emissions.

Published in	International Journal of Statistical Distributions and Applications (Volume 8, Issue 2)
DOI	10.11648/j.ijsd.20220802.11
Page(s)	24-29
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), 2022. Published by Science Publishing Group

Keywords

Gaussian Density Function, Fugitive Emissions, Agricultural Waste, Rail Transportation, Pollutant Concentrations

References

[1]	Ahmad, H., Khan, T. A., Durur, H., Ismail, G. M. & Yokus, A. (2021). Analytic Approximate Solutions of Diffusion Equations Arising in Oil Pollution, Journal of Ocean Engineering and Science, 6 (1), 62-69, ISSN 2468-0133, https://doi.org/10.1016/j.joes.2020.05.002
[2]	Akanbi, O. B. & Oladoja, O. M. (2018). Bayesian Analysis of 2014 FIFA World Cup Matches Played and Goals Scored. International Journal of Modern Mathematical Sciences, Florida, USA, 16 (1): 25 - 36.
[3]	Akanbi, O. B. & Oladoja, O. M. (2019). Application of a Modified g-Parameter Prior in Bayesian Model Averaging to CO₂ Emissions in Nigeria. Mathematical Theory and Modeling, 9 (11): 57-71.
[4]	Akanbi, O. B., Oladoja, O. M. & Udomboso, C. G. (2019). Bayesian Approach to Survival Modeling of Remission Duration for Acute Leukemia. International Journal of Engineering Science and Computing, 9 (3): 20165-20167.
[5]	Baragano, D., Ratie, G., Sierra, C., Chrastny, V., Komarek, M. & Gallego, J. R. (2022). Multiple Pollution Sources Unraveled by Environmental Forensics Techniques and Multivariate Statistics. Journal of Hazardous Materials, 424 (127413).
[6]	Baran, S., Szokol, P. & Szabo, M. (2021). Truncated Generalized Extreme Value Distribution-based Ensemble Model Output Statistics Model for Calibration of Wind Speed Ensemble Forecasts. Environmetrics, https://doi.org/10.1002/env.2678.
[7]	Barnett, V. (2004). Environmental Statistics: Methods and Applications. West Sussex: John Wiley & Sons, Ltd.
[8]	Green, A. E, Singhal, R. P. & Venkateswar, R. (1980). Analytic Extensions of the Gaussian Plume Model, Journal of the Air Pollution Control Association, 30: 7, 773-776, DOI: 10.1080/00022470.1980.10465108.
[9]	Gui, C. & Zhao, M. (2015). Traveling Wave Solutions of Allen–Cahn Equation with a Fractional Laplacian. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 32 (4), 785-812, ISSN 0294-1449, https://doi.org/10.1016/j.anihpc.2014.03.005.
[10]	Hariharan, G. (2014). An Efficient Legendre Wavelet-Based Approximation Method for a Few Newell–Whitehead and Allen–Cahn Equations. J Membrane Biol 247, 371–380. https://doi.org/10.1007/s00232-014-9638-z
[11]	Javeed, S., Saif, S., Waheed, A. & Baleanu, D. (2018). Exact Solutions of Fractional mBBM Equation and Coupled System of Fractional Boussinesq-Burgers, Results in Physics, 9, 1275-1281, ISSN 2211-3797, https://doi.org/10.1016/j.rinp.2018.04.026.
[12]	Ott, W. R. (1995). Environmental Statistics and Data Analysis. New York: Lewis Publishers. 191-295.
[13]	Patel, H., Patel, T. & Pandit, D. (2022). An Efficient Technique for Solving Fractional-order Diffusion Equations Arising in Oil Pollution. Journal of Ocean Engineering and Science. https://doi.org/10.1016/j.joes.2022.01.004
[14]	Raftery, A. E., Madigan, D. & Hoeting, J. A. (1997). Bayesian Model Averaging for Linear Regression Models. Journal of the American Statistical Association, 92: 179-191.
[15]	Raftery, A. E., Gneiting, T., Balabdaoui, F. & Polakowski, M. (2005). Using Bayesian Model Averaging to calibrate forecast ensembles. Mon. Wea. Rev} 133: 1155-1174.
[16]	Raftery, A. E., Painter, I. S. & Volinsky, C. T. (2005). BMA: An R Package for Bayesian Model Averaging. R News, 5: 2-8.
[17]	Reimann, R. C., Filzmoser, P., Garrett, R. G. & Dutter, R. (2008). Statistical Data Analysis Explained: Applied Environmental Statistics. West Sussex: John Wiley & Sons, Ltd.
[18]	Tattar, P. N., Ramaiah, S. & Manjunath, B. G. (2016). A Course in Statistics with R. John Wiley & Sons.
[19]	Sala-i-Martin, X. X., Doppelhofer, G. & Miller, R. I. (2004). Determinants of Long Term Growth: A Bayesian Averaging of Classical Estimates (BACE) approach. American Economic Review, 94: 813-835.
[20]	Sloughter, J. M. Raftery, A. E., Gneiting, T. & Fraley, C. (2007). Probabilistic Quantitative Precipitation Forecasting using Bayesian Model Averaging. Mon. Wea. Rev., 135: 3209-3220.
[21]	Smith, R. L, Tebaldi, C., Nychka, D. & Mearns, L. O. (2009). Bayesian Modeling of Uncertainty in ensembles of climate models. J. Amer. Stat. Assoc., 104: 97-111.
[22]	Soch, J., Meyer, A. P., Haynes, J. & Allefeld, C. (2017). How to improve parameter estimates in GLM-based fMRI data analysis: cross-validated Bayesian Model Averaging. NeuroImage.
[23]	Tian, X., Xie, Z., Wang, A. & Yang, X. (2012). A new approach for Bayesian Model Averaging. Sci. China Earth Sci., 55: 136-1344.
[24]	Tsangarides, C. G. (2005). Growth Empirics under Model Uncertainty: Is Africa Different? IMF Working Paper 05/18, Washington, DC, USA.
[25]	Vehtari, A., Gelman, A. & Gabry, J. (2016). Practical Bayesian Model Evaluation using Leave-one-out cross validation and WAIC. arXiv: 1507.04544v5 [stat.CO], 1-28.
[26]	Yeung, K. Y., Fraley, C., Young, W. C., Bumgarner, R. & Raftery, A. E. (2014). Bayesian Model Averaging methods and R Package for Gene Network Construction. Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York City, USA.

Cite This Article

Plain Text BibTeX RIS

APA Style

Kazeem Olalekan Obisesan, Oladapo Muyiwa Oladoja. (2022). On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria. International Journal of Statistical Distributions and Applications, 8(2), 24-29. https://doi.org/10.11648/j.ijsd.20220802.11

Copy | Download

ACS Style

Kazeem Olalekan Obisesan; Oladapo Muyiwa Oladoja. On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria. Int. J. Stat. Distrib. Appl. 2022, 8(2), 24-29. doi: 10.11648/j.ijsd.20220802.11

Copy | Download

AMA Style

Kazeem Olalekan Obisesan, Oladapo Muyiwa Oladoja. On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria. Int J Stat Distrib Appl. 2022;8(2):24-29. doi: 10.11648/j.ijsd.20220802.11

Copy | Download

@article{10.11648/j.ijsd.20220802.11,
  author = {Kazeem Olalekan Obisesan and Oladapo Muyiwa Oladoja},
  title = {On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {8},
  number = {2},
  pages = {24-29},
  doi = {10.11648/j.ijsd.20220802.11},
  url = {https://doi.org/10.11648/j.ijsd.20220802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20220802.11},
  abstract = {Normal processes produce random variables with a normal distribution, which is the most important model in statistics. Due to the constant speed and direction of the carrier medium, a continuous source releases particles like environmental pollutants in drift be it in the air, water or soil. By differentiating the normal density function, this study used the knowledge of the plume model to build two separate paths of utilizing Gaussian probability density function with mean of zero to show that it meets the diffusion equation from physical principles through the knowledge of a Brownian motion in monitoring emissions of carbon monoxide from different sources in the most populous black country. Carbon monoxide emissions from manufacturing industries and construction (MIC), fugitive emissions from solid fuels (FESO), and agricultural waste burning (AWB) are all higher than other sources in Nigeria, according to this research. Rail transportation (RAIL) is the lowest source of carbon monoxide emissions, and pollution diffusion in the country follows a predictable pattern in form of a normal process. The magnitude of the standard deviations affects the precision of confidence intervals used to estimate mean pollutant concentrations. Decision-makers in the country will know which sectors to focus on in order to reduce carbon monoxide emissions.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria
AU  - Kazeem Olalekan Obisesan
AU  - Oladapo Muyiwa Oladoja
Y1  - 2022/05/10
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsd.20220802.11
DO  - 10.11648/j.ijsd.20220802.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 24
EP  - 29
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20220802.11
AB  - Normal processes produce random variables with a normal distribution, which is the most important model in statistics. Due to the constant speed and direction of the carrier medium, a continuous source releases particles like environmental pollutants in drift be it in the air, water or soil. By differentiating the normal density function, this study used the knowledge of the plume model to build two separate paths of utilizing Gaussian probability density function with mean of zero to show that it meets the diffusion equation from physical principles through the knowledge of a Brownian motion in monitoring emissions of carbon monoxide from different sources in the most populous black country. Carbon monoxide emissions from manufacturing industries and construction (MIC), fugitive emissions from solid fuels (FESO), and agricultural waste burning (AWB) are all higher than other sources in Nigeria, according to this research. Rail transportation (RAIL) is the lowest source of carbon monoxide emissions, and pollution diffusion in the country follows a predictable pattern in form of a normal process. The magnitude of the standard deviations affects the precision of confidence intervals used to estimate mean pollutant concentrations. Decision-makers in the country will know which sectors to focus on in order to reduce carbon monoxide emissions.
VL  - 8
IS  - 2
ER  -

Copy | Download

Author Information

Kazeem Olalekan Obisesan

Department of Statistics, University of Ibadan, Ibadan, Nigeria
Oladapo Muyiwa Oladoja

Department of Mathematics and Statistics, First Technical University, Ibadan, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Kazeem Olalekan Obisesan, Oladapo Muyiwa Oladoja. (2022). On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria. International Journal of Statistical Distributions and Applications, 8(2), 24-29. https://doi.org/10.11648/j.ijsd.20220802.11

Copy | Download

ACS Style

Kazeem Olalekan Obisesan; Oladapo Muyiwa Oladoja. On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria. Int. J. Stat. Distrib. Appl. 2022, 8(2), 24-29. doi: 10.11648/j.ijsd.20220802.11

Copy | Download

AMA Style

Kazeem Olalekan Obisesan, Oladapo Muyiwa Oladoja. On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria. Int J Stat Distrib Appl. 2022;8(2):24-29. doi: 10.11648/j.ijsd.20220802.11

Copy | Download

@article{10.11648/j.ijsd.20220802.11,
  author = {Kazeem Olalekan Obisesan and Oladapo Muyiwa Oladoja},
  title = {On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {8},
  number = {2},
  pages = {24-29},
  doi = {10.11648/j.ijsd.20220802.11},
  url = {https://doi.org/10.11648/j.ijsd.20220802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20220802.11},
  abstract = {Normal processes produce random variables with a normal distribution, which is the most important model in statistics. Due to the constant speed and direction of the carrier medium, a continuous source releases particles like environmental pollutants in drift be it in the air, water or soil. By differentiating the normal density function, this study used the knowledge of the plume model to build two separate paths of utilizing Gaussian probability density function with mean of zero to show that it meets the diffusion equation from physical principles through the knowledge of a Brownian motion in monitoring emissions of carbon monoxide from different sources in the most populous black country. Carbon monoxide emissions from manufacturing industries and construction (MIC), fugitive emissions from solid fuels (FESO), and agricultural waste burning (AWB) are all higher than other sources in Nigeria, according to this research. Rail transportation (RAIL) is the lowest source of carbon monoxide emissions, and pollution diffusion in the country follows a predictable pattern in form of a normal process. The magnitude of the standard deviations affects the precision of confidence intervals used to estimate mean pollutant concentrations. Decision-makers in the country will know which sectors to focus on in order to reduce carbon monoxide emissions.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - On Normal Process of Diffusion Equation in Monitoring Carbon Monoxide Concentrations in Nigeria
AU  - Kazeem Olalekan Obisesan
AU  - Oladapo Muyiwa Oladoja
Y1  - 2022/05/10
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsd.20220802.11
DO  - 10.11648/j.ijsd.20220802.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 24
EP  - 29
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20220802.11
AB  - Normal processes produce random variables with a normal distribution, which is the most important model in statistics. Due to the constant speed and direction of the carrier medium, a continuous source releases particles like environmental pollutants in drift be it in the air, water or soil. By differentiating the normal density function, this study used the knowledge of the plume model to build two separate paths of utilizing Gaussian probability density function with mean of zero to show that it meets the diffusion equation from physical principles through the knowledge of a Brownian motion in monitoring emissions of carbon monoxide from different sources in the most populous black country. Carbon monoxide emissions from manufacturing industries and construction (MIC), fugitive emissions from solid fuels (FESO), and agricultural waste burning (AWB) are all higher than other sources in Nigeria, according to this research. Rail transportation (RAIL) is the lowest source of carbon monoxide emissions, and pollution diffusion in the country follows a predictable pattern in form of a normal process. The magnitude of the standard deviations affects the precision of confidence intervals used to estimate mean pollutant concentrations. Decision-makers in the country will know which sectors to focus on in order to reduce carbon monoxide emissions.
VL  - 8
IS  - 2
ER  -

Copy | Download