Observed advantage for negative binomial over Poisson distribution in partial duration series |
| |
| Authors: | A Ben-Zvi |
| |
| Institution: | (1) Israel Hydrological Service, P.O. Box 6381, 91063 Jerusalem, Israel |
| |
| Abstract: | The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year
–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events. |
| |
| Keywords: | Hydrology runoff partial duration series negative binomial distribution Poisson distribution |
| 本文献已被 SpringerLink 等数据库收录！ |
|
