A Robust Approach for Best Probability Distribution Model Selection for Optimal Analysis of Radio Signals

Full Text (PDF, 726KB), PP.57-67

Views: 0 Downloads: 0


Joseph Isabona 1,* Osaghae Edgar 1 Agbotiname Lucky Imoize 2 Ikechi Irisi 3

1. Department of Physics, Federal University Lokoja, PMB.1154, Kogi State, Lokoja, Nigeria

2. Department of Electrical and Electronics Engineering, Faculty of Engineering, University of Lagos, Akoka, Lagos 100213, Nigeria

3. Department of Physics, River State University, Port Harcourt, River State, Nigeria

* Corresponding author.

DOI: https://doi.org/10.5815/ijwmt.2022.04.05

Received: 6 Apr. 2022 / Revised: 11 May 2022 / Accepted: 21 May 2022 / Published: 8 Aug. 2022

Index Terms

Stochastic radio signals, Parametric models, Density functions, Distribution functions, Reliability, Probabilistic modeling.


Probabilistic parametric functions such as density and distribution functions modeled to depict certain stochastic behaviour are used to express the fundamental theories of reliability engineering. In the existing works of literature, a few probability distribution functions have been well reported. However, selecting and identifying the most suitable distribution functions to reliably model and fit datasets remain. This work examines the application of three different methods for selecting the best function to model and fit measured data. The methods comprise the parametric maximum likelihood estimation, Akaike Information Criteria and the Bayesian Information Criteria. In particular, these methods are implemented on Signal Interference to Noise Ratio (SINR) data acquired over an operational Long Term Evolution (LTE) mobile broadband networks in a typical built-up indoor and outdoor campus environment for three months. Generally, results showed a high level of consistency with the Kolmogorov-Semirnov Criteria. Specifically, the Weibull distribution function showed the most credible performance for radio signal analysis in the three study locations. The explored approach in this paper would find useful applications in modeling, design and management of cellular network resources

Cite This Paper

Joseph Isabona, Osaghae Edgar, Agbotiname Lucky Imoize, Ikechi Irisi, "A Robust Approach for Best Probability Distribution Model Selection for Optimal Analysis of Radio Signals", International Journal of Wireless and Microwave Technologies(IJWMT), Vol.12, No.4, pp. 57-67, 2022. DOI:10.5815/ijwmt.2022.04.05


[1]A. Ikuta, and H. Orimoto, Stochastic Signal Processing for Sound Environment System with Decibel Evaluation and Energy Observation, Mathematical Problems in Engineering, vol. 2014, pp.1-8, 2014. http://dx.doi.org/10.1155/2014/208612

[2]Isabona, and C.C. Konyeha, Urban Area Path loss Propagation Prediction and Optimization Using Hata Model at 800MHz. IOSR Journal of Applied Physics (IOSR-JAP), vol. 3, pp. 8-18, 2013

[3]J. Isabona, and D. O. Ojuh, Radio Link Quality measurement Survey over HSDPA Radio Interface: A Holistic Technique for Efficient Networks Performance Monitoring in Wireless Communication Systems, Nigerian Journal of Physics, vol. 25 (2), pp. 46-54, 2013.

[4]J. Isabona, and S. Azi, Measurement, Modeling and Analysis of Received Signal Strength at 800MHz and 1900MHz in Antenna Beam Tilt Cellular Mobile Environment, Elixir Comp. Sci. & Engg. 54 (2013) 12300-12303

[5]A. Ikuta, H. Masuike, and M. Ohta, “A digital filter for stochastic systems with unknown structure and its application to psychological evaluation of sound environment,” IEICE Transactions on on Information and Systems, vol. 88, no. 7, pp. 1519–1525, 2005

[6]V. Bartkute, and L. Sakalauskas L. The methods of the three-parameter Weibull distribution estimation. Acta et commentationes Universitatis tartuensis de mathematica, vol. 12, pp. 65-78, 2008.

[7]R. Luus, and M, Jammer, Estimation of Parameters in 3-parameter Weibull probability distribution functions, Hungarian Journal of industrial Chemistry Vesprem. vol.33 (1-2), pp.69-73, 2005.

[8]U. Singh, P.K, Gupta and S.K. Upadhyay, Estimation of three-parameter exponentiated-Weibull distribution under type-II censoring. Journal of statistical planning and inference, vol.134, pp. 350-372, 2005.

[9]R. Luus, and M, Jammer, Estimation of Parameters in 3-parameter Weibull probability distribution functions, Hungarian Journal of industrial Chemistry Vesprem. vol. 33 (1-2), pp.69-73, 2005.

[10]D. Markovic, D. Jukic, and M. Bensic, Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, Journal of Computational and Applied Mathematics. vol. 228, pp.304–312, 2009.

[11]H. Nagatsuka, H. A study of estimation for the three-parameter Weibull distribution based on doubly Type-II censored data using a least squares method. Proceedings of the 2008 Second International Conference on Secure System Integration and Reliability Improvement, pp. 158–165, 2008.

[12]D. Cousineau, Nearly unbiased estimators for the three-parameter Weibull distribution with greater efficiency than the iterative likelihood method. Brit. J. Math. Statist. Psychol. vol. 62, pp. 167–191, 2009

[13]G. Jin G, Q. Liu, J.L.Zhou, and Z.B. Zhou Z.B., RePofe: Reliability physics of failure estimation based on stochastic performance degradation for the momentum wheel. Engineering Failure Analysis, vol. 22, pp. 50-63, 2012.

[14]G. Jin G, D. Matthews, Y. Fan and Q. Liu, Physics of failure-based degradation modelling and lifetime prediction of the momentum wheel in a dynamic covariate environment. Engineering Failure Analysis, vol. 28, pp. 222-240, 2013 

[15]R.F. Atta-Elmanan, and K.B.F. Mohammed, Reliability Analysis using Weibull Distribution Kiln of Alsalam Cement Factory as Case Study, International Journal of Science and Research (IJSR), vol. 5(5), pp. 1196-1198, 2015.

[16]D.I, Dumitrascu, C.O. Morariu, A.E Dumitrascu, and D.V. Ciobanu, Reliability Estimation of Towed Grader Attachment Using Finite Element Analysis and Point Estimation,  Transactions of Famena, vol. XLII-1, pp. 85-98, 2018.

[17]J. Isabona, Maximum likelihood Parameter based Estimation for In-depth Prognosis Investigation of Stochastic Electric Field Strength Data, BIU Journal of Basic and Applied Sciences, vol. 4(1): 127 – 136, 2019.

[18]Langat, P.K; Kumar, L and Koech, R. (2019). Identification of the Most Suitable Probability Distribution Models for Maximum, Minimum, and Distribution Models for Maximum, Minimum, and Mean Streamflow, Water, 11, 734. doi:10.3390/w11040734.

[19]A. Rao, and K. Hamed, The logistic distribution. In Flood Frequency Analysis; CRC Press: Boca Raton, FL, USA, pp. 291–321, 2000.

[20]A. Boisbunon, S. Canu, D, D. Fourdrinier, W. Strawderman, M.T. Wells. "Akaike's Information Criterion, Cp and estimators of loss for elliptically symmetric distributions", International Statistical Review, vol. 82, pp. 422–439, doi:10.1111/insr.12052.

[21]K.P. Burnham, and D. RAnderson, D. R. "Multimodel inference: understanding AIC and BIC in Model Selection", Sociological Methods & Research, vol. 33, pp. 261–304, 204.  doi:10.1177/0049124104268644.

[22]X. Gao and P. Song, P. "Composite likelihood Bayesian information criteria for model selection in high-dimensional data". Journal of the American Statistical Association. vol. 105 (492), pp. 1531–1540, 2010. doi:10.1198/jasa.2010.tm09414.

[23]X. Gao, and R. J.  Carroll, (2017). "Data integration with high dimensionality". Biometrika. vol. 104, pp. 251–272, 2017. doi:10.1093/biomet/asx023. PMC 5532816

[24]Martinez, W. L.; Martinez, A. R. & Solka, J. (2010). Exploratory Data Analysis with MATLAB, second edition.   Chapman & Hall/CRC. ISBN 9781439812204

[25]Divine O. Ojuh, Joseph Isabona, (2021). Empirical and Statistical Determination of Optimal Distribution Model for Radio Frequency Mobile Networks Using Realistic Weekly Block Call Rates Indicator “. International Journal of Mathematical Sciences and Computing (IJMSC), vol. 7, no. 3, pp. 12-23, 2021. doi: 10.5815/ijmsc.2021.03.02

[26]Joseph Isabona, Divine O. Ojuh," Machine Learning Based on Kernel Function Controlled Gaussian Process Regression Method for In-depth Extrapolative Analysis of Covid-19 Daily Cases Drift Rates ", International Journal of Mathematical Sciences and Computing (IJMSC), vol.7, no.2, pp. 14-23, 2021. doi: 10.5815/ijmsc.2021.02.02

[27]Divine O. Ojuh, Joseph Isabona, "Field Electromagnetic Strength Variability Measurement and Adaptive Prognostic Approximation with Weighed Least Regression Approach in the Ultra-high Radio Frequency Band", International Journal of Intelligent Systems and Applications (IJISA), vol.13, no.4, pp.14-23, 2021. doi: 10.5815/ijisa.2021.04.02

[28]J. Isabona, and D.O Ojuh, ‘‘Modelling based Quantitative Assessment of Operational LTE Mobile Broadband Networks Reliability: a Case Study of University Campus Environ’’, IOSR Journal of Electronics and Communication Engineering (IOSR-JECE), vol. 15(1). pp. 22-31,2020

[29]V,C. Ebhota, J. Isabona and V.M. Srivastava, V.M. ‘‘Environment-Adaptation Based Hybrid Neural Network Predictor for Signal Propagation Loss, Prediction in Cluttered and Open Urban Microcells’’, Wireless Personal Communications, vol. 104 (3), pp. 935–948

[30]J. Isabona Wavelet Generalized Regression Neural Network Approach for Robust Field Strength Prediction. Wireless Personal Communications, vol. 114, pp. 3635–3653 (2020). https://doi.org/10.1007/s11277-020-07550-55.