A Family of Lifetime Distributions

Table 1

Parameter estimates, values of the log-likelihood (LL) and Akaike information criterion (AIC), and Kolmogorov-Smirnov (K-S) statistic obtained from the fit of each of the four distributions, to the times of first failure of devices (data set 1) and the machine’s subsystems lifetimes (data set 2).

Data set	Distribution	𝜃=(𝛼,𝛽,𝜆,𝑝)	LL	AIC	K-S (P value)
1(𝑛=50)	EXTG	(14.06,.4838,.042,313.57)	227.25	462.50	.1470(.2300)
	XTG	(13.747,.588,.00876,---)	231.65	469.29	.1597(.1562)
	Chen	(---,.3444,.0205,---)	233.17	470.34	.1676(.1204)
	DAL	(6.2975,.8074,.0053,---)	236.04	478.08	.1981(.03945)
2(𝑛=44)	EXTG	(.0831,.2007,.0211,20.4087)	348.01	704.02	.1397(.3262)
	XTG	(.0806,.2086,.0057,---)	351.43	708.86	.1667(.1544)
	Chen	(---,.2473,.0024,---)	351.25	706.50	.1737(.1244)
	DAL	(1.752,.7771,.0021,---)	359.44	724.89	.2875(.0001)