Extreme value theory

SUMMARY Estimation of the occurance probabilities of extreme incidents has a vital importance in many science fields. The distributions which were used by German mathematician Emil Julis Gumbel in the 1950s, are recently and rapidly developing topics of statistics. The first applications were to answer environmental questions and quickly have followed by the finance industry. Besides, since the distribution of data of internet network, structural reliability and biotechnic analysis are heavy tailed, they have become the main targets of EVT applications. Natural disasters have threatened the world and they will so. Moreover, the fast development of industry and technology contribute to the damage caused by natural disasters. When compared with the ones happened in the past, natural disasters happening now, cause to more damage. As a result of rapidly growing populations, villages turn into towns and towns into metropolis which leads to the establishment of residental and industrial areas without measuring the disaster risks. Any natural disaster likely to occour in such areas might cause a great deal of destruction. In this study, the data of the earthquakes which occured in our country between the years 1976 and 2003 has been used. The data has been taken from the records kept by Kandilli Observatory. By using this data, the probabilities of earthquakes ranging between 4 and 7,4 have been calculated with Extreme Value Theory, Moments Method, Maximum Likelihood, Incompleted Means Method. Key Words : Earthquake, Extreme Value Theory, Moments Method, Maximum Likelihood Method, Incompleted Means Method. n