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Classes of Ordinary Differential Equations Obtained for the Probability Functions of Linear Failure Rate and Generalized Linear Failure Rate Distributions

Okagbue, H. I. and Oguntunde, P.E. and Opanuga, A. A. and Adamu, Patience I. (2018) Classes of Ordinary Differential Equations Obtained for the Probability Functions of Linear Failure Rate and Generalized Linear Failure Rate Distributions. International Journal of Circuits, Systems and Signal Processing, 12. pp. 596-603. ISSN 1998-4464

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Abstract

The linear failure rate (hazard) and generalized linear failure rate (hazard) distributions are uniquely identified by their linear hazard functions. In this paper, homogenous ordinary differential equations (ODES) of different orders were obtained for the probability functions of linear failure rate and generalized linear failure rate distributions. This is possible since the aforementioned probability functions of the distributions are differentiable and the former distribution is a particular case of the later. Differentiation and modified product rule were used to derive the required ODEs, whose solutions are the respective probability functions. The different conditions necessary for the existence of the ODEs were obtained and it is 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 one considered in this research. Algorithms for implementation can be helpful in improving the results.

Item Type: Article
Uncontrolled Keywords: Differentiation, product rule, quantile function, failure rate, approximation, hazard function, inverse survival function.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Mrs Patricia Nwokealisi
Date Deposited: 20 Jun 2018 08:37
Last Modified: 20 Jun 2018 08:37
URI: http://eprints.covenantuniversity.edu.ng/id/eprint/10967

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