2018
DOI: 10.1007/s11277-018-6090-x
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Closed Form Expressions for the Quantile Function of the Erlang Distribution Used in Engineering Models

Abstract: 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 distribu… Show more

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Cited by 5 publications
(3 citation statements)
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“…A comparison with the machine values was done to evaluate the efficiency and the performance of the quantile models obtained. Recently, authors [ 54 ] applied the same methodology proposed in this paper to obtained the near exact quantile values for the Erlang distribution. Unfortunately, the results cannot be applied to the gamma distribution since Erlang is a subset of the gamma distributions.…”
Section: Gamma Distributionmentioning
confidence: 99%
See 1 more Smart Citation
“…A comparison with the machine values was done to evaluate the efficiency and the performance of the quantile models obtained. Recently, authors [ 54 ] applied the same methodology proposed in this paper to obtained the near exact quantile values for the Erlang distribution. Unfortunately, the results cannot be applied to the gamma distribution since Erlang is a subset of the gamma distributions.…”
Section: Gamma Distributionmentioning
confidence: 99%
“…Erlang distribution considers only the cases of gamma, where the shape parameter is a positive integer. The implication is that the result of [ 54 ] cannot be applied when the shape parameter is not a positive integer.…”
Section: Gamma Distributionmentioning
confidence: 99%
“…Approximation remains the only viable option to use in obtaining a function that closely resembles the closed-form expression for the QF. Approximation in this context is the use of numerical optimization, although other methods such as functional approximation, the use of series expansions are available [8][9][10][11].…”
Section: Introductionmentioning
confidence: 99%