Closed Form Expressions for the Quantile Function of the Erlang Distribution Used in Engineering Models
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Quantile function is heavily utilized in modeling, 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 (CDF). As a result, approximation
becomes the other option. The failure of the inversion method is often due to the
intractable nature of the CDF of the distribution. Erlang distribution belongs to those
classes of distributions. The distribution is a particular case of the gamma distribution.
Little is known about the quantile approximation of the Erlang distribution. This is due
to the fact that researchers prefer to work with the gamma distribution of which the
Erlang is a particular case. This work applied the quantile mechanics approach, power
series method and cubic spline interpolation to obtain the approximate of the quantile
function of the Erlang distribution for degrees of freedom from one to two. The
approximate values compares favorably with the exact ones. Consequently, the result in
this paper improved the existing results on the extreme tails of the distribution. The
closed form expression for the quantile function obtained here is very useful in
modeling physical and engineering systems that are completely described by or fitted
with the Erlang distribution
Keywords
Q Science (General)