Fig 1.
Plot of the recorded earth quack observed worldwide concerning the earthquake magnitude.
Here, the point sizes will increase concerning the magnitude. The bigger magnitude means a bigger plot of that dataset.
Fig 2.
Plot of the recorded volcano eruption all over the world map concerning the number of days volcano eruption happened.
The larger the triangle is, the larger the volcanic eruption time as per the dataset.
Fig 3.
Plot of the absolute mean magnitude of earthquake vs mean period of volcano eruption.
The use of the absolute mean of the earthquake’s magnitude nearby vs the mean of the volcano’s duration for the observed earthquake count near the volcano. The threshold distance is 100 km and three years. The polynomial regression is used with 7 degrees to plot(for 5 degree polynomial regression fit, R2 is 0.341).
Fig 4.
The use of the median of the earthquake’s magnitude nearby vs the Median of the volcano’s duration is used as per the dataset we created.
The threshold distance is 100 km and three years. The multiple R2 is 0.1597. Then it is used the polynomial regression with 7 degrees to plot( polynomial regression fit, R2 is 0.159).
Table 1.
Kolmogorov–Smirnov-test for every count with respect to the model 1, from where the men and variances are estimated
Fig 5.
Plot of volcanic eruption duration(logarithmic transformation) for counts of earthquake happened within 100 km and three years of the volcano.
Here, it is considered that the earthquake count of 3, 4, 6 and 10. here, the red line indicates the sample drawn from normal distribution from the proposed model given in the model 1. It is statistically verify that the model 1 assumption is valid for all the cases (Table 1). see Remark 4 for detailed explanation.
Fig 6.
This plot illustrates one instance of creating the dataset.
Then plotted the location (latitude, longitude) of 1 typical volcano (Rincon De Vieja), indicated by the Red Triangle, and the earthquake that happened near its 100 km (denoted with the blue circles) that happened in the coastal area of U.S.
Fig 7.
Plot of the arithmetic mean magnitude of earthquake vs period of volcano eruption.
The arithmetic mean of the earthquake’s magnitude nearby vs the volcano’s duration is used. The threshold distance is 100 km and three years. Here (x, y) is defined as (arithmetic mean of earthquake magnitude, volcano duration). Here the estimated variance is σx = 0.0985, and σy = 3.75 and the covariance ρ is 0.00901. The two parameters are taken with logarithmic transformation. Fitting Bivariate normal distribution, used the Anderson- Darling test, which gives the p-value = 9.999e−5 and the Cramer Von Mises test gives the same p-value = 9.999e−5.
Table 2.
Watson Test Result for Dataset of Volcano Eruption and Earthquake dataset for 0.01 level of Significance both of location parameters of the dataset does not follow a von Mises distribution.
Table 3.
Test of Homogeneity to get if both the location parameters of the Volcano Eruption and Earthquake dataset follow the same distribution or not.
Table 4.
Hypothesis test for von Mises-Fisher distribution over Kent distribution for earthquake dataset where the p-value is 0.583 and the null hypothesis is whether a von Mises-Fisher distribution fits the data well, where the alternative is that Kent distribution is more suitable and similar for volcano dataset where the p-value of this dataset is 0.5270.
Table 5.
This table contains the partition of the combined earthquake and volcano dataset, which givesseven partitions that follow Vonmises distribution considering the projection of the location parameter and Individually tested the distributions of that dataset with the help of Watson Test.
Fig 8.
Plot of the volcano part of the dataset all over the two-dimensional world map with the densities.
Fig 9.
Plot of the volcano part of the dataset all over the three-dimensional world map with the density.
Fig 10.
Plot of the earthquake part of the dataset all over the spherical world map with the densities.
Fig 11.
Plot of the earthquake part of the dataset all over the two-dimensional world map with the densities.
Table 6.
Table containing the Bayesian Information Criteria Score for Each K value. From that, 14 partitions can provide a mixture of Fisher Von Mises Distribution for the location parameter(Longitude and Latitude together). Then checked 20 values of k from 1 to 20, where the optimal number of partitions is 14.
Table 7.
Table containing the Bayesian Information Criteria Score for Each K value. From that, 14 partitions can provide a mixture of Fisher Von Mises Distribution for the location parameter(Longitude and Latitude together). Checked 20 values of k from 1 to 20, and the optimal number of partitions is 14. Then, used the earthquake part of the combined dataset to get this table.