| Author | Uruya Leeyavanija |
| Call Number | AIT Thesis no. WA-84-10 |
| Subject(s) | Hydrology--Mathematical models
|
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Abstract | The quantile and sextile methods as new parameter estimation techniques
for the gamma--type distributions have been developed in this study. Extensive Monte Carlo experiments are conducted to evaluate the performance of six fitting methods for different sample sizes and different combinations of population
statistics.
The applicability of the proposed methods is examined by choosing the Pearson Type 3 (P3) and Log Pearson Type 3 (LP3) distributions as representatives of gamma-type distributions. Performance evaluation of the better
fitting technique has been done by using two performance criteria; the first is the root mean square error (RMSE) of estimates of quantiles corresponding to six probability levels, and the second is the bias of estimated distribution parameters as well as estimated quantiles. The performance of the better fitting procedure is also evaluated when the observations are drawn
from other than the gamma-type distributions to assess the robustness of the methods.
Monte Carlo results show that no method generally produces the unbiased estimators of both P3 and LP3 distribution parameters. However, on average, the sextile method seems to produce a relatively smaller bias of estimators
than the others. Of hydrologic concern is the accuracy with which the fitted distributions give rise to good estimates of various quantiles (e.g. T-year
design magnitudes). It follows from this performance criterion that the method of quantiles coupling with the maximum likelihood estimators is the
best for all quantile estimates, except for the median quantile for which the
method of sextiles is the best, when the observations a re highly skewed (i.e., the skew is larger than 1.0) for the P3 distribution. In the application of the LP3 distribution, the method of quantiles coupling with the
method using the first two moments in real space yields the most accurate estimates of high extreme quantiles with probability levels larger than
0.99 for highly variable and skewed data sequences (the coefficients of variation and skewness are ·equal to 0.66 and·: 3.95,: respectively). |
| Year | 1983 |
| Type | Thesis |
| School | School of Engineering and Technology |
| Department | Department of Civil and Infrastucture Engineering (DCIE) |
| Academic Program/FoS | Water Resources Research Engineering (WA) |
| Chairperson(s) | Hoshi, Kiyoshi |
| Examination Committee(s) | Huynh, Ngoc Phien ; Rahman, Md. Ataur
|
| Scholarship Donor(s) | The Government of Netherlands |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 1983 |