Figure 1

The mixture distribution used to generate the data:

Table 1

The actual values of theta for the 50k sample we took from the mixture distribution:

thresh_tests n_overthresh theta
50 14069 0.28138
100 2838 0.05676
150 812 0.01624
250 144 0.00288
500 16 0.00032
750 4 0.00008
1000 2 0.00004

Figure 2

Figure 3

Introduce the numerical estimation thing with the simple lomax:

Figure 4

Bias correction

Nonparametric bootstrap correction for both the GLM Lomax and GP