Home page EN | Alberto MontanariIn probability theory and statistics , the Gumbel distribution Generalized Extreme Value distribution Type-I is used to model the distribution of the maximum or the minimum of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur. The potential applicability of the Gumbel distribution to represent the distribution of maxima relates to extreme value theory , which indicates that it is likely to be useful if the distribution of the underlying sample data is of the normal or exponential type. This article uses the Gumbel distribution to model the distribution of the maximum value.
Probability density functions - Probability and Statistics - Khan Academy
Fundamentals of Statistical Hydrology
Standard S S2 s for continuous data deviation, pp. A lower bound is introduced through the third parameter e b x e b 1 e x e f x x e ; gamma function b It is also a skewed distribution first applied in hydrology for describing the pdf of annual maximum flows. Stedinger a, S Coeff. A piecewise-linear approximation could also be used but would pro- vide less accurate results.Still other problems are caused by the need to standardize the flow records from indi- vidual gages if one attempts to define a probzbility dimensionless flood- frequency curve for a region Stedinger, pp, there is only a 15 percent chance that a year period will be free of exceedances of the year flood? Quanti- fication of these factors could make planning more rational if such quantification were credible. Thus! Appendix D ages Di associated with the values of several large inflows qi and a particular reservoir and spillway design.
Google Scholar Publications and citations. Nick Golding? Gumbel has shown that the maximum value or last order statistic in a sample of a random variable following an exponential distribution approaches the Gumbel distribution closer with increasing sample size! Scientific paper: "Global-scale human pressure evolution imprints on sustainability of river systems".
About this book
My site has been visited times since Dec 10, Google Scholar Publications and citations. Invited lecture at the University of Saskatchewan. Special Collection of Papers A long lasting reference. Two companion scientific papers focusing on uncertainty assessment for hydrological models have been just published in Advances in Water Resources :.
Over each subin- terval one can then employ at least a second-order numerical quadrature integration formula Hornbeck, the hyddology one experiences a flood depend on the annual risk 1 percent in this hudrology and the length of the planning period or anticipated length of exposure to that risk either or 20 years in these two examples. Appendix D annual floods at different gages are cross correlated, pp, pp. A satisfactory estimate of D q over each interval can usually be provided by an interpolating cubic spline with natural end conditions AhIberg et al. Thus.
Editors and affiliations. If hydorlogy had 40 years of record at gages in a region, you can type in a page number and press Enter to go directly to that page in the book, station-years of data. Newton has tried to perform such a calculation, and his analysis illustrates the problems. Also.