A New Probability Heavy-Tail Model for Stochastic Modeling under Engineering Data

Table 2

E (X), Var (X), Skew (Y), and Kur (Y) of the GOLLRW model.

a1	a2	a3	E (Y)	Var (Y)	Skew (Y)	Kur (Y)
5	3	5	1.345101	0.00505689	0.6318044	5.061672
15	30	10	1.457796	0.00016184	0.1697300	4.254602
10	10	10	1.306376	0.00029275	0.2534783	4.321513
3	3	3	1.662868	0.06496940	1.446316	9.454736
6	2	4	1.307624	0.00517879	0.584800	4.970088
4	10	1.25	8.880579	6.72013100	2.530743	31.17977
20	1	1.25	1.343270	0.00498280	0.3517877	4.511826
5	5	25	1.082753	0.00012864	0.4177994	4.468587
5	4	2	2.435783	0.10874430	1.098394	7.35003
10	4	2	2.410562	0.02529735	0.5168014	4.862499
5	3.25	110	1.014244	5.922422 × 10^−6	−7.363551	3226.473
5	3.25	110	1.014928	5.850545 × 10^−6	−1.786044	911.3018
5	3	2	2.10945	0.08155823	1.0983940	7.35003
		3	1.641584	0.02132604	0.8260043	5.833843
		4	1.449212	0.00923430	0.7025623	5.317628
		5	1.345101	0.00505689	0.6318044	5.061672
		10	1.159385	0.00092786	0.4951955	4.687103
		50	1.029963	2.945824 × 10^−5	−2.294597	512.6364
		55	1.027201	2.428456 × 10^−5	−3.185613	747.5396
		60	1.024905	2.037847 × 10^−5	−4.239300	1052.191
		65	1.022967	1.735751 × 10^−5	−5.470000	1438.862
		75	1.019874	1.305848 × 10^−6	−8.510591	2509.386
		80	1.01862	1.149769 × 10^−6	−10.34218	3219.91
		100	1.014867	7.449114 × 10^−6	−19.95313	7553.195
		110	1.013506	6.209712 × 10^−6	−26.22742	10810.18
25	0.5	2.5	0.877862	0.00033823	0.2040570	3.038384
	1		1.158345	0.00058918	0.1803159	4.161341
	5		2.205088	0.00213523	0.1778989	4.276042
	10		2.909631	0.00371766	0.1778995	4.276013
	50		5.538931	0.01347241	0.1778979	4.276089
	100		7.308664	0.02345683	0.1778996	4.276008
5	2	1.5	2.072792	0.14499560	1.4195490	9.958146
10			2.038083	0.03241762	0.6331623	5.224646
15			2.031779	0.01411739	0.4139129	4.630934
20			2.029582	0.00788481	0.3083409	4.43794
30			2.028015	0.00348664	0.2045775	4.304321
50			2.027214	0.00125194	0.1224461	4.237321
60			2.027076	0.00086901	0.1019976	4.225757
70			5.10 × 10^−5	4.10933900	1.0001580	1.000521