## 1 Introduction
They reported that the use of the generic parameters for the forecast model leads to the overestimation of the seismic activity. One of the critical tasks in statistical seismology is the ability to accurately and reliably forecast the evolution of earthquake sequences. A consistent approach for earthquake forecast testing has been implemented in the Collaboratory for the Study of Earthquake Predictability (CSEP) [16; 17; 18; 19]. In this framework, the gridded rate forecast is used in which the selected geographic area is separated into zones then the number of earthquakes in each zone is estimated [19]. In addition, the number of earthquakes in each forecast bin is considered to be independent of the other bins and follows the Poisson distribution. Several statistical tests were developed as part of the CSEP framework to examine earthquake forecasts. As a result of these developments, it is possible to determine if a particular forecasting scheme is able to accurately replicate locations, magnitudes, and the observed numbers of earthquakes [19; 20]. Various forecasting algorithms can also be compared using the aforementioned likelihood-based tests. For example, retrospective aftershock forecasting of the 2011 Tohoku, Japan; 2010 Canterbury, New Zealand; 2016 Kaikoura, New Zealand; and 2019 Ridgecrest, California earthquakes were tested by using this approach [21; 22; 23; 24]. In this study, the analysis of three major earthquake sequences that occurred in Alaska in the past 20 years was conducted to test retrospectively the ability to forecast the magnitudes of the largest expected aftershocks. Specifically, the 23 January 2018 Mw 7.9 Kodiak earthquake occurred in the Gulf of Alaska near Kodiak Island at 09:31:40.89 UTC at a depth of 14 km [25; 26]. There was no significant damage reported. The earthquake woke residents in Anchorage which was located 560 km northeast from the epicenter. It was also felt in parts of British Columbia, Canada. The 2018 Mw 7.1 Anchorage earthquake happened approximately 15 km north from Anchorage, Alaska on 30 November of 2018 at 17:29:29.33 UTC at a depth of 46.7 km [9; 27]. A few minutes later, a magnitude 5.8 aftershock shook the region. Significant damage has been reported to infrastructure, buildings, and airports [9]. Moreover, we investigated the characteristics of the 3 November 2002, Mw 7.9 Denali earthquake that occurred in central Alaska along a shallow strike-slip fault on the Denali-Totschunda fault system [28; 29]. The details of the selected mainshocks are listed in Table 1 and the spatial distributions of the mainshocks with the corresponding aftershock sequences during the first 14 days are shown in Figure 1.  
In this study, the left truncated exponential distribution was utilized to model the magnitude frequency statistics [30]. Moreover, the modified Omori-Utsu (OU) law [31] and Epidemic Type Aftershock Sequence (ETAS) model [32] were used to approximate the rate of the aftershocks. In addition, two statistical approaches including the extreme value distribution and Bayesian predictive distribution were utilized to compute the probabilities of having the largest expected aftershocks to be above a certain magnitude during the evolution of each sequence. The paper is structured as follows: Section 2 begins with the specification of the earthquake catalogues and follows by defining the statistical methods to analyze the aftershock sequences. The results of the statistical analysis are provided in Section 3. In Section 4, discussion of the results and concluding remarks are given. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Name** & **Date** & **Time** & **Latitude** & **Longitude** & **Magnitude** & **Depth** \\ \hline Denali & 3 November 2002 & 22:12:41 & 63.5141 & \(-\)147.4529 & 7.9 Mw & 4.2 km \\ Kodiak & 23 January 2018 & 09:31:40 & 56.0039 & \(-\)149.1658 & 7.9 Mw & 14 km \\ Anchorage & 30 November 2018 & 17:29:29 & 61.3464 & \(-\)149.9552 & 7.1 Mw & 46.7 km \\ \hline \end{tabular}
\end{table}