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Half-Cauchy and Power Cauchy Distributions: 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-Cauchy and power Cauchy distributions. 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-Cauchy and power Cauchy distributions 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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Acknowledgements

This work was supported by Covenant University, Nigeria.

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Authors and Affiliations

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

    Hilary I. Okagbue, Patience I. Adamu, Sheila A. Bishop & Ezinne C. Erondu

  2. Department of Mathematics, University of Lagos, Akoka, Nigeria

    Muminu O. Adamu

Authors
  1. Hilary I. Okagbue
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  2. Muminu O. Adamu
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  3. Patience I. Adamu
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  4. Sheila A. Bishop
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  5. Ezinne C. Erondu
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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., Adamu, M.O., Adamu, P.I., Bishop, S.A., Erondu, E.C. (2019). Half-Cauchy and Power Cauchy Distributions: 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_26

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  • DOI: https://doi.org/10.1007/978-981-13-2191-7_26

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