The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences

Table 8

MLEs of the proposed model parameters, the goodness-of-fit tests, and the p values (in parenthesis) for Data Set I.

Distributions
Estimates (SEs)		W	A
AT-W ()	= 2.383 (0.204)	0.475	2.595	0.187 (0.035)
	= 0.011 (0.001)
Weibull (α, )		0.548	2.987	0.184 (0.039
	= 0.012(0.001)
Burr-XII (α, )		0.228	1.328	0.295 (0.0001)
	= 0.225(0.062)
	= 36.285(3.870)
Beta-Weibull (α, )	= 6.754(2.562)	0.273	1.467	0.293 (0.0001)
	= 0.128(0.024)
	= 1.164(0.058)
Kappa (α, )	= 10.050(1.051)	0.503	2.754	0.353 (0.032)
	= 5.745(48.933)
	= 77.672(0.584)