Journal of Probability and Statistics / 2023 / Article / Tab 4 / Research Article
Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails Table 4 Summary statistics for the PL estimator for different parameter values
and different sample lengths of the series
with long-range dependence semi-Poisson Lévy-based process.
N True value 2 0.8 0.2 3 1.6 0.6 1.3 3 0.3 100 Mean 1.8161 0.8414 0.1329 3.1862 1.2904 0.6178 1.3012 2.8738 0.2210 Bias 0.1838 −0.0414 0.0671 −0.1862 0.3096 −0.0178 −0.0012 0.1261 0.3 MSE 0.0654 0.0209 0.0574 0.0346 0.0958 0.0003 0.0280 0.0359 0.09 250 Mean 1.9398 0.8203 0.2081 3.0856 1.2957 0.5884 1.2911 2.973 0.3410 Bias 0.0601 −0.0203 −0.0081 −0.0855 0.3043 0.0115 −0.0000 0.0269 0.0003 MSE 0.0077 0.0140 0.0044 0.0283 0.0104 0.0077 0.0000 0.0209 0.0000 500 Mean 2.0032 0.8111 0.2029 3.0065 1.5594 0.6222 1.3001 3.0001 0.3041 Bias 0.0223 0.0102 0.0011 −0.0064 0.0004 0.0081 0.0000 0.0000 0.0000 MSE 0.0049 0.0079 0.0021 0.0038 0.0058 0.0031 0.0000 0.0000 0.0000 N True value 1.5 1 0.6 1 0.4 0.2 3 0.6 0.9 30 Mean 1.6158 0.8636 0.4518 0.9091 0.6454 0.1524 3.3537 0.5939 0.7143 Bias −0.1158 0.1363 0.1482 0.0908 −0.2454 0.0475 −0.3536 0.0060 0.1856 MSE 0.0383 0.0478 0.0541 0.0354 0.0751 0.0448 0.1274 0.0072 0.0561 500 Mean 1.5808 0.8860 0.6172 0.9671 0.3774 0.1899 3.0793 0.6211 0.8059 Bias −0.0807 0.1139 −0.0172 0.0328 0.0225 −0.0022 −0.0792 −0.0211 0.0740 MSE 0.0065 0.0380 0.0241 0.0010 0.0005 0.0000 0.0064 0.0124 0.0160 1000 Mean 1.5025 0.9933 0.6002 0.9953 0.4029 0.2001 3.0431 0.6065 0.9026 Bias −0.0025 0.0766 0.0053 −0.0000 0.0000 0.0000 −0.0431 −0.0056 0.0167 MSE 0.0000 0.0058 0.0000 0.0000 0.0000 0.0000 0.0027 0.0021 0.0042