Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model

Table 2

ARB and RMSE of five estimated parameters (𝛼₁,𝛼₂,𝛽,𝜆₁,and𝜆₂) and AUC, when 𝛼₁=2, 𝛼₂=3, 𝜆₁=1, and 𝜆₂=1 and with different values of 𝛽.

(𝑚,𝑛)	MLE	𝛽=2	𝛽=2.5	𝛽=3
(50, 50)	𝛼1	0.1925 (1.7453)	0.1646 (1.7159)	0.1863 (1.7626)
	𝛼2	0.4685 (2.245)	0.3917 (1.9021)	0.4641 (2.348)
	𝛽	0.0554 (0.6402)	0.0912 (0.7801)	0.0558 (0.9117)
	𝜆1	0.1044 (0.5624)	0.0700 (0.5442)	0.0800 (0.5353)
	𝜆2	0.1048 (0.5779)	0.0746 (0.5624)	0.0939 (0.5719)
	AUC	0.0067 (0.0556)	0.0026 (0.0557)	0.0036 (0.0529)
(50, 80)	𝛼1	0.2538 (1.8319)	0.2472 (2.0245)	0.2775 (2.0910)
	𝛼2	0.2818 (2.0819)	0.2691 (2.245)	0.3046 (2.3255)
	𝛽	0.0401 (0.5415)	0.0557 (0.6907)	0.0475 (0.8629)
	𝜆1	0.0825 (0.4706)	0.0635 (0.4821)	0.0815 (0.4803)
	𝜆2	0.0724 (0.4790)	0.0489 (0.4931)	0.0741 (0.4952)
	AUC	0.0045 (0.0490)	0.0015 (0.0510)	0.0008 (0.050)
(80, 50)	𝛼1	0.1846 (1.6341)	0.2311 (1.7011)	0.2874 (1.7425)
	𝛼2	0.2515 (2.2201)	0.3733 (2.2412)	0.3969 (1.956)
	𝛽	0.0501 (0.4921)	0.0414 (0.701)	0.0339 (0.8101)
	𝜆1	0.0380 (0.4365)	0.0665 (0.4577)	0.0905 (0.4761)
	𝜆2	0.0443 (0.4681)	0.0952 (0.5278)	0.0962 (0.5221)
	AUC	0.0003 (0.0479)	0.0013 (0.0479)	0.0055 (0.0489)
(80, 80)	𝛼1	0.162 (1.3518)	0.1531 (1.3652)	0.1594 (1.3561)
	𝛼2	0.2096 (1.8697)	0.2047 (3.9241)	0.1655 (2.183)
	𝛽	0.0372 (0.4715)	0.0438 (0.5934)	0.0458 (0.7095)
	𝜆1	0.0464 (0.4011)	0.0404 (0.3996)	0.0433 (0.4048)
	𝜆2	0.0488 (0.4211)	0.0417 (0.4334)	0.0291 (0.4084)
	AUC	0.002 (0.0412)	0.0023 (0.0424)	0.003 (0.0435)