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Half-Normal Distribution: Ordinary Differential Equations

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Transactions on Engineering Technologies (WCECS 2017)

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Abstract

In this chapter, homogenous ordinary differential equations (ODES) of different orders were obtained for the probability density function, quantile function , survival function inverse survival function , hazard function and reversed hazard functions of half-normal distribution . This is possible since the aforementioned probability functions are differentiable. Differentiation and modified product rule were used to obtain the required ordinary differential equations, whose solutions are the respective probability functions. The different conditions necessary for the existence of the ODEs were obtained and it is almost in consistent with the support that defined the various probability functions considered. The parameters that defined each distribution greatly affect the nature of the ODEs obtained. This method provides new ways of classifying and approximating other probability distributions apart from half-normal distribution considered in this chapter. In addition, the result of the quantile function can be compared with quantile approximation using the quantile mechanics .

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References

  1. G. Steinbrecher, W.T. Shaw, Quantile mechanics. Euro. J. Appl. Math. 19(2), 87–112 (2008)

    Article  MathSciNet  Google Scholar 

  2. H.I. Okagbue, M.O. Adamu, T.A. Anake, Quantile approximation of the chi-square distribution using the quantile mechanics, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 477–483

    Google Scholar 

  3. H.I. Okagbue, M.O. Adamu, T.A. Anake, Solutions of chi-square quantile differential equation, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 813–818

    Google Scholar 

  4. Y. Kabalci, On the Nakagami-m inverse cumulative distribution function: closed-form expression and its optimization by backtracking search optimization algorithm. Wireless Pers. Comm. 91(1), 1–8 (2016)

    Article  Google Scholar 

  5. W.P. Elderton, Frequency Curves and Correlation (Charles and Edwin Layton, London, 1906)

    MATH  Google Scholar 

  6. N. Balakrishnan, C.D. Lai, Continuous Bivariate Distributions, 2nd edn. (Springer, New York, London, 2009)

    MATH  Google Scholar 

  7. N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous Univariate Distributions, vol. 2. 2nd edn (Wiley, 1995)

    Google Scholar 

  8. N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous Univariate Distributions (Wiley, New York, 1994). ISBN: 0-471-58495-9

    Google Scholar 

  9. H. Rinne, Location scale distributions, linear estimation and probability plotting using MATLAB (2010)

    Google Scholar 

  10. H.I. Okagbue, P.E. Oguntunde, A.A. Opanuga, E.A. Owoloko, Classes of ordinary differential equations obtained for the probability functions of Fréchet distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 186–191

    Google Scholar 

  11. H.I. Okagbue, P.E. Oguntunde, P.O. Ugwoke, A.A. Opanuga, Classes of ordinary differential equations obtained for the probability functions of exponentiated generalized exponential distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 192–197

    Google Scholar 

  12. H.I. Okagbue, A.A. Opanuga, E.A. Owoloko, M.O. Adamu, Classes of ordinary differential equations obtained for the probability functions of cauchy, standard cauchy and log-cauchy distributions, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 198–204

    Google Scholar 

  13. H.I. Okagbue, S.A. Bishop, A.A. Opanuga, M.O. Adamu, Classes of ordinary differential equations obtained for the probability functions of Burr XII and Pareto distributions, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 399–404

    Google Scholar 

  14. H.I. Okagbue, M.O. Adamu, E.A. Owoloko, A.A. Opanuga, Classes of ordinary differential equations obtained for the probability functions of Gompertz and Gamma Gompertz distributions, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 October, 2017 (San Francisco, U.S.A., 2017), pp. 405–411

    Google Scholar 

  15. H.I. Okagbue, M.O. Adamu, A.A. Opanuga, J.G. Oghonyon, Classes of ordinary differential equations obtained for the probability functions of 3-parameter Weibull distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 539–545

    Google Scholar 

  16. H.I. Okagbue, A.A. Opanuga, E.A. Owoloko, M.O. Adamu, Classes of ordinary differential equations obtained for the probability functions of exponentiated Fréchet distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 546–551

    Google Scholar 

  17. H.I. Okagbue, M.O. Adamu, E.A. Owoloko, S.A. Bishop, Classes of ordinary differential equations obtained for the probability functions of Half-Cauchy and power Cauchy distributions, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 552–558

    Google Scholar 

  18. H.I. Okagbue, P.E. Oguntunde, A.A. Opanuga, E.A. Owoloko, Classes of ordinary differential equations obtained for the probability functions of exponential and truncated exponential distributions, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 858–864

    Google Scholar 

  19. H.I. Okagbue, O.O. Agboola, P.O. Ugwoke, A.A. Opanuga, Classes of Ordinary differential equations obtained for the probability functions of exponentiated Pareto distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 865–870

    Google Scholar 

  20. H.I. Okagbue, O.O. Agboola, A.A. Opanuga, J.G. Oghonyon, Classes of ordinary differential equations obtained for the probability functions of Gumbel distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 871–875

    Google Scholar 

  21. H.I. Okagbue, O.A. Odetunmibi, A.A. Opanuga, P.E. Oguntunde, Classes of ordinary differential equations obtained for the probability functions of half-normal distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 876–882

    Google Scholar 

  22. H.I. Okagbue, M.O. Adamu, E.A. Owoloko, E.A. Suleiman, Classes of ordinary differential equations obtained for the probability functions of Harris extended exponential distribution, in Lecture Notes in Engineering and Computer Science: Proceedings of the World Congress on Engineering and Computer Science, 25–27 Oct 2017 (San Francisco, U.S.A., 2017), pp. 883–888

    Google Scholar 

  23. H.I. Okagbue, M.O. Adamu, T.A. Anake, Ordinary differential equations of the probability functions of weibull distribution and their application in ecology. Int. J. Engine. Future Tech. 15(4), 57–78 (2018)

    Google Scholar 

  24. A. Pewsey, Large-sample inference for the general half-normal distribution. Comm. Stat. Theo. Meth. 31(7), 1045–1054 (2002)

    Article  MathSciNet  Google Scholar 

  25. A. Pewsey, Improved likelihood based inference for the general half-normal distribution. Comm. Stat. Theo. Meth. 33(2), 197–204 (2004)

    Article  MathSciNet  Google Scholar 

  26. A.G. Nogales, P. Perez, Unbiased estimation for the general half-normal distribution. Comm. Stat. Theo. Meth. 44(7), 3658–3667 (2015)

    Article  MathSciNet  Google Scholar 

  27. J.J. Duarte Sanchez, W.W. da Luz Freitas, G.M. Cordeiro, The extended generalized half-normal distribution. Braz. J. Prob. Stat. 30(3), 366–384 (2016)

    Article  MathSciNet  Google Scholar 

  28. R.R. Pescim, C.G.B. Demétrio, G.M. Cordeiro, E.M.M. Ortega, M.R. Urbano, The beta generalized half-normal distribution. Comput. Stat. Data Anal. 54(4), 945–957 (2010)

    Article  MathSciNet  Google Scholar 

  29. K. Cooray, M.M.A. Ananda, A generalization of the half-normal distribution with applications to lifetime data. Comm. Stat. Theo. Methods 37(9), 1323–1337 (2008)

    Article  MathSciNet  Google Scholar 

  30. W.J. Huang, N.C. Su, A study of generalized normal distributions. Comm. Stat. Theo. Methods 46(11), 5612–5632 (2017)

    Article  MathSciNet  Google Scholar 

  31. A.W. Kemp, The discrete half-normal distribution, in Advances in Mathematical and Statistical Modeling (Birkhäuser, Boston), pp. 353–360

    Chapter  Google Scholar 

  32. N.M. Olmos, H. Varela, H.W. Gómez, H. Bolfarine, An extension of the half-normal distribution. Stat. Papers 53(4), 875–886 (2012)

    Article  MathSciNet  Google Scholar 

  33. G.M. Cordeiro, R.R. Pescim, E.M.M. Ortega, The Kumaraswamy generalized half-normal distribution for skewed positive data. J. Data Sci. 10(2), 195–224 (2012)

    MathSciNet  Google Scholar 

  34. T. Ramires, E.M. Ortega, G.M. Cordeiro, G. Hamedani, The beta generalized half-normal geometric distribution. Studia Scient. Math. Hunga. 50(4), 523–554 (2013)

    MATH  Google Scholar 

  35. A. Alzaatreh, K. Knight, On the gamma half-normal distribution and its applications. J. Modern Appl. Stat. Methods 12(1), 103–119 (2013)

    Article  Google Scholar 

  36. W. Gui, An alpha half-normal slash distribution for analyzing non negative data. Comm. Stat. Theo. Methods 44(22), 4783–4795 (2015)

    Article  MathSciNet  Google Scholar 

  37. L.M. Castro, H.W. Gómez, M. Valenzuela, Epsilon half-normal model: properties and inference. Comput. Stat. Data Anal. 56(12), 4338–4347 (2012)

    Article  MathSciNet  Google Scholar 

  38. G.M. Cordeiro, E.M.M. Ortega, G.O. Silva, The exponentiated generalized gamma distribution with application to lifetime data. J. Stat. Comput. Simul. 81(7), 827–842 (2011)

    Article  MathSciNet  Google Scholar 

  39. B.Y. Murat, J. Ahad, F.Z. Dogru, O. Arslan, The generalized half-t distribution. Stat. Interf. 10(4), 727–734 (2017)

    Article  MathSciNet  Google Scholar 

  40. G.M. Cordeiro, M. Alizadeh, R.R. Pescim, E.M. Ortega, The odd log-logistic generalized half-normal lifetime distribution: properties and applications. Comm. Stat. Theo. Methods 46(9), 4195–4214 (2017)

    Article  MathSciNet  Google Scholar 

  41. D.O. Cahoy, Minkabo, Inference for three-parameter M-Wright distributions with applications. Model. Assist. Stat. Appl. 12(2), 115–125 (2017)

    Google Scholar 

  42. A.G. Glen, L.M. Leemis, D.J. Luckett, Survival distributions based on the incomplete gamma function ratio, in Proceedings Winter Simulation Conference, Article. Number 7822105 (2017)

    Google Scholar 

  43. C.Y. Chou, H.R. Liu, Properties of the half-normal distribution and its application to quality control. J. Industr. Technol. 14(3), 4–7 (1998)

    Google Scholar 

  44. G. Lang, The difference between wages and wage potentials: earnings disadvantages of immigrants in Germany. J. Econ. Inequal. 3(1), 21–42 (2005)

    Article  Google Scholar 

  45. F.P. Schoenberg, R. Peng, J. Woods, On the distribution of wildfire sizes. Environmetrics 14(6), 583–592 (2003)

    Article  Google Scholar 

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Acknowledgements

This work was supported by Covenant University, Ota, Nigeria.

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Authors and Affiliations

  1. Department of Mathematics, Covenant University, Ota, Nigeria

    Hilary I. Okagbue, Oluwole A. Odetunmibi, Sheila A. Bishop, Pelumi E. Oguntunde & Abiodun A. Opanuga

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  1. Hilary I. Okagbue
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  2. Oluwole A. Odetunmibi
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  3. Sheila A. Bishop
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  4. Pelumi E. Oguntunde
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  5. Abiodun A. Opanuga
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Correspondence to Hilary I. Okagbue .

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Editors and Affiliations

  1. International Association of Engineers, Hong Kong, Hong Kong

    Sio-Iong Ao

  2. Department of Computer and Communication, Daegu Catholic University, Daegu, Korea (Republic of)

    Haeng Kon Kim

  3. University of New Orleans, New Orleans, LA, USA

    Mahyar A. Amouzegar

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Okagbue, H.I., Odetunmibi, O.A., Bishop, S.A., Oguntunde, P.E., Opanuga, A.A. (2019). Half-Normal Distribution: Ordinary Differential Equations. In: Ao, SI., Kim, H., Amouzegar, M. (eds) Transactions on Engineering Technologies. WCECS 2017. Springer, Singapore. https://doi.org/10.1007/978-981-13-2191-7_14

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  • DOI: https://doi.org/10.1007/978-981-13-2191-7_14

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