Entropy-based parameter estimation for extended Burr XII distribution.

*(English)*Zbl 1416.62124Summary: Two entropy-based methods, called ordinary entropy (ENT) method and parameter space expansion method (PSEM), both based on the principle of maximum entropy, are applied for estimating parameters of the extended Burr XII distribution. With the parameters so estimated, the Burr XII distribution is applied to six peak flow datasets and quantiles (discharges) corresponding to different return periods are computed. These two entropy methods are compared with the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood estimation (MLE). It is shown that PSEM yields the same quantiles as does MLE for discrete cases, while ENT is found comparable to the MOM and PWM. For shorter return periods (\(<\)10–30 years), quantiles (discharges) estimated by these four methods are in close agreement, but the differences amongst them grow as the return period increases. The error in quantiles computed using the four methods becomes larger for return periods greater than 10–30 years.

##### MSC:

62E15 | Exact distribution theory in statistics |

62P12 | Applications of statistics to environmental and related topics |

60E05 | Probability distributions: general theory |

##### Keywords:

principle of maximum entropy; flood frequency analysis; probability weighted moments; methods of moments; maximum likelihood estimation
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\textit{Z. Hao} and \textit{V. P. Singh}, Stoch. Environ. Res. Risk Assess. 23, No. 8, 1113--1122 (2009; Zbl 1416.62124)

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