Abstract: This paper provides an introduction to multivariate non-parametric hazard model for the occurrence of earthquakes since the hazard function defines the statistical distribution of inter-event times. The method is ap plied to the Turkish seismicity since a significant portion of Turkey is subject to frequent earthquakes and presents several advantages compared to other more traditional approaches. Destructive earthquakes from 1903 to 2009 between the longitudes of (39-42)N◦ and the latitudes of (26-45)E◦ are used. The paper demonstrates how seismicity and tectonics/physics parameters that can potentially influence the spatio-temporal variability of earthquakes and presents several advantages compared to more traditional approaches.
The statistical modeling of natural disasters is an indispensable tool for extracting information for prevention and risk reduction casualties. The Poisson distribution can reveal the characteristics of 1 a natural disaster. However, this distribution is insufficient for the clustering of natural events and related casualties. The best approach is to use a Neyman type A (NTA) distribution which has the feature that two or more events occur in a short time. We obtain some properties of the NTA distribution and suggest that it could provide a suitable description to analyze the natural disaster distribution and casualties. We support this argument using disaster events, including earthquakes, floods, landslides, forest fires, avalanches, and rock falls in Turkey between 1900 and 2013. The data strongly supports that the NTA distribution represents the main tool for handling disaster data. The findings indicate that approximately three earthquakes, fifteen landslides, five floods, six rock falls, six avalanches, and twenty nine forest fires are expected in a year. The results from this model suggest that the probability of the total number of casualties is the highest for the earthquakes and the lowest for the rock falls. This study also finds that the expected number of natural disasters approximately equals to 64 per year and inter-event time between two successive earthquakes is approximately four months. The inter-event time for the natural disasters is approximately six days in Turkey.
Abstract: In this study, first exit time of a compound Poisson process with positive jumps and an upper horizontal boundary is considered. An explicit formula is derived for the mean first exit time associated with the compound Poisson process. Finally, an application on traffic accidents is given to illustrate the usage of the mean first exit time.
In this paper, we introduce a new four-parameter distribution called the transmuted Weibull power function (TWPF) distribution which e5xtends the transmuted family proposed by Shaw and Buckley . The hazard rate function of the TWPF distribution can be constant, increasing, decreasing, unimodal, upside down bathtub shaped or bathtub shape. Some mathematical properties are derived including quantile functions, expansion of density function, moments, moment generating function, residual life function, reversed residual life function, mean deviation, inequality measures. The estimation of the model parameters is carried out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using real data sets.