Nature inspired quantile estimates of the Nakagami distribution
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Description
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.
Keywords
Q Science (General)