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Quantile Approximation of the Erlang Distribution using Differential Evolution Algorithm

Okagbue, H. I. and Adamu, M. O. and Anake, T. A. and Wusu, Ashiribo S. (2020) Quantile Approximation of the Erlang Distribution using Differential Evolution Algorithm. International Journal of Advanced Trends in Computer Science and Engineering, 9 (3). ISSN 2278-3091

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Erlang distribution is a particular case of the gamma distribution and is often used in modeling queues, traffic congestion in wireless sensor networks, cell residence duration and finding the optimal queueing model to reduce the probability of blocking. The application is limited because of the unavailability of closed-form expression for the quantile (inverse cumulative distribution) function of the distribution. The problem is primarily tackled using approximation since the inversion method cannot be applied. This paper extended a six parameter quantile model earlier proposed to the Nakagami distribution to the Erlang distributions. Consequently, the established relationship between the two distributions is now extended to their quantile functions. The quantile model was used to fit the machine (R software) values with their corresponding quartiles in two ways. Firstly, artificial neural network (ANN) was used to establish that a curve fitting can be achieved. Lastly, differential evolution (DE) algorithm was used to minimize the errors obtained from the curve fitting and hence estimate the values of the six parameters of the quantile model that will ensure the best possible fit, for different values of the parameters that characterize Erlang distribution. Hence, the problem is constrained optimization in nature and the DE algorithm was able to find the different values of the parameters of the quantile model. The simulation result corroborates theoretical findings. The work is a welcome result for the quest for a universal quantile model that can be applied to different distributions.

Item Type: Article
Uncontrolled Keywords: Artificial Neural Networks, Differential Evolution, curve fitting, Quantile function, Erlang; Nakagami; queue, statistics.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Mrs Patricia Nwokealisi
Date Deposited: 17 Jun 2021 10:24
Last Modified: 17 Jun 2021 10:24

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