Chen, GemaiKim, Hyang MiJi, Chaoqun2013-07-102013-11-122013-07-102013Ji, C. (2013). Analysis of Temporally Dependent Extremes for the Gumbel Distribution (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24824http://hdl.handle.net/11023/796For modeling extremal behaviors, the Generalized extreme value distribution that originated from the well established Extreme Value Theory has been widely used. As a special case of such Generalized extreme value distribution, the Gumbel family is suitable for modeling maximum values from light-tailed distributions. A common assumption used in the central models of extreme values is the independence of extremes in most previous studies. However, short-term dependence among extremes might exist. In this thesis, we study a linear Gumbel distributed autoregressive model which was introduced by Toulemonde et al. (2010) to simulate dependent extremes that follow the Gumbel distribution. Our main goal is to investigate that if Gumbel distributed short-term maxima are weakly/moderately/strongly dependent, but this dependence is not recognized, what will happen to the resulting estimates of the Gumbel parameters. To reach this goal, simulations and a numerical example in environmental science are presented to quantify the above issue.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.StatisticsGumbel distributiondependent extreme valuesmaster thesis10.11575/PRISM/24824