Stochastic earthquake interevent time modeling from exponentiated Weibull distributions

Stochastic modelling of earthquake interoccurrence times in Northwest Himalaya and adjoining regions

“…The shape of the exponentiated Weibull distribution (Figure 3) agrees well to the gamma, Weibull, and exponentiated exponential; yet it is more generic and demands further investigations (Mudholkar and Srivastava 1993;Dikshit 2015b, 2018). The exponentiated Weibull density and hazard rate function, irrespective of small or large t, can be well approximated by a simple two-parameter Weibull model (Mudholkar and Srivastava 1993;Pasari and Dikshit 2018). Apart from the hazard function, the mean residual life (MRL) function and its asymptotic behaviour of the exponentiated Weibull model also characterizes earthquake hazard analysis in a large seismotectonic province (Pasari 2015;Pasari and Dikshit 2018).…”

“…The exponentiated Weibull density and hazard rate function, irrespective of small or large t, can be well approximated by a simple two-parameter Weibull model (Mudholkar and Srivastava 1993;Pasari and Dikshit 2018). Apart from the hazard function, the mean residual life (MRL) function and its asymptotic behaviour of the exponentiated Weibull model also characterizes earthquake hazard analysis in a large seismotectonic province (Pasari 2015;Pasari and Dikshit 2018). Therefore, the present study comprising the recently used exponentiated models illumines better insights to the hazard assessment and contributes to the development of innovative methods in earthquake hazard analysis in the northwest Himalaya and its adjacent regions.…”

“…Particularly, when shape parameter(s) takes unit value, all of gamma, Weibull, exponentiated exponential, and exponentiated Weibull distributions turns out to a single-parameter time-independent exponential distribution (Johnson et al 1995). Similarly, it may be observed that exponential, Rayleigh, Weibull, exponentiated exponential and exponentiated Rayleigh (Burr Type X) distributions belong to the sub-families of the exponentiated Weibull distribution (Mudholkar and Srivastava 1993;Pasari and Dikshit 2018). In terms of hazard shapes, gamma, Weibull, and exponentiated exponential distributions offer monotone (increasing, decreasing, and constant) hazard functions, whereas the lognormal, inverse Gaussian, inverse Weibull, exponentiated Rayleigh, and exponentiated Weibull distributions provide monotone as well as non-monotone hazard shapes; Rayleigh distribution has only increasing hazard shapes, and the heavy-tailed Pareto distribution offers only decreasing hazard shapes (Johnson et al 1995).…”

“…Thus, to overcome these shortcomings of conventional models and to bridge the gap between physical and statistical models in seismology, a series of generalizations and modifications have taken place. Some notable examples are the generalized gamma distribution (Bak et al 2002), triple exponential distribution (Kijko and Sellevoll 1981), heavy-tailed Pareto distribution (Kagan and Schoenberg 2001;Ferraes 2003), inverse Gaussian or the Brownian passage time distribution (Matthews et al 2002;Pasari and Dikshit 2015b), Rayleigh distribution (Ferraes 2003), inverse Weibull (Frechet) distribution Dikshit 2014a, 2015a), and the most recent exponentiated group of distributions, such as the exponentiated exponential, exponentiated Rayleigh, and the exponentiated Weibull distributions (Pasari and Dikshit 2014b, 2015a, 2015b, 2018. Though these distributions, as a whole, serve most of the requirements of seismologists and earthquake professionals, it is still unclear which distribution is the globally best model and whether that one will remain as the best in future also.…”

Evaluation of the Conditional Probability of January 24, 2020 Sivrice (Elazığ) Earthquake

“…Bu nedenle bölgede farklı magnitütlü depremler için tekrarlama periyotları incelenmeli ve deprem tehlikesi güncel verilerle değerlendirilmelidir. Deprem tehlikesini belirlemek için deterministik ve olasılıksal yöntemler kullanılmaktadır [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. İstatistiksel dağılım modelleri farklı bölgelerdeki deprem tehlikesini belirlemek için olasılıksal yöntemler içeresinde kullanılmıştır [13][14][15][16][17][18][19][20][21][22][23].…”