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Nature inspired quantile estimates of the Nakagami distribution

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Abstract

Nakagami-m distribution is utilized heavily in modelling multipath interferences in wireless networks. However, the closed form of the quantile function of the distribution is not available. The unavailability of the closed form is a result of the intractable nature of the cumulative distribution function (CDF). Hence, the inversion method cannot be used to recover the quantile function (QF) from the CDF of Nakagami-m distribution. Approximation is often the only choice available and numerical optimization method is one of the new forms of quantile approximation. This work proposed a new quantile model which is used to fit the machine values of QF of some selected parameters of the distribution. Differential evolution was used to minimize the error that resulted from the curve fitting. The resulting model is an appreciably improvement over some existing ones found in literature, using the root mean square error as the performance metric. In addition, the precision of the model increases as the shape parameter of the distribution decreases and the model was able to capture the extreme tails of the distribution better than the other previous published results. Thereafter, the usefulness of the model was seen in random number generation and Monte Carlo simulation. Anderson–Darling test showed that the simulated random variables are not from the normal distribution, despite the huge sample size. Different aspects of wireless communications will benefit from the applications of this work.

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Acknowledgements

The serene environment provided by Covenant University was one the variables that facilitated the conduct of this research.

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Authors and Affiliations

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

    Hilary I. Okagbue & Timothy A. Anake

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

    Muminu O. Adamu

  3. Department of Mathematics, Lagos State University, Ojo, Lagos, Nigeria

    Ashiribo S. Wusu

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  1. Hilary I. Okagbue
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  2. Muminu O. Adamu
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Correspondence to Hilary I. Okagbue.

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Okagbue, H.I., Adamu, M.O., Anake, T.A. et al. Nature inspired quantile estimates of the Nakagami distribution. Telecommun Syst 72, 517–541 (2019). https://doi.org/10.1007/s11235-019-00584-6

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