Closed form expression for the inverse cumulative distribution function of Nakagami distribution
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Abstract
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Quantile function or inverse cumulative
distribution function (CDF) is heavily utilized in
modelling, simulation, reliability analysis and
random number generation. The use is often
limited if the inversion method fails to estimate it
from the cumulative distribution function. As a
result, approximation becomes the other feasible
option. The failure of the inversion method is often
due to the intractable nature of the CDF of the
distribution. Approximation may come in the form
of series expansions, closed form or functional
approximation, numerical algorithm and the closed
form expression drafted in terms of the quantile
function of another distribution. This work used the
cubic spline interpolation to obtain the closed form of the inverse cumulative distribution function of
the Nakagami-m distribution. Consequently, the
closed form of the quantile function obtained for
the selected parameters of the distribution serves as
an approximation which compares favourably with
the R software values. The result obtained was a
significant improvement over some results surveyed
from literature for four reasons. Firstly, the
approximates produced better results in simulation
as evidenced by the some values of the root mean
square error of this work when compared with
others. Secondly, the result obtained at the extreme
tail of the distribution is better than others selected
from the literature. Thirdly, the closed form
estimates are easy to compute and save
computation time. The closed form of the quantile
function obtained in this work can be used in
simulating Nakagami random variables which are
used in modelling attenuation and fading channels
in wireless communications and ultrasonic tissue
characterization.
Keywords
QA Mathematics