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Table 1 Summary statistics for the MLE of θ under Case 1: γ and τ are known

From: The linearly decreasing stress Weibull (LDSWeibull): a new Weibull-like distribution

True values

Sample size

MLE summary statistics

(θ0,γ0,τ0)

n

Bias

Variance

MSE

CV (%)

(1, 2.1, 4)

10

2.0031×10−01

1.4643×10−01

1.87×10−01

31.9

 

100

2.5252×10−02

7.7759×10−03

8.41×10−03

8.6

(5, 2.1, 0.5)

10

6.6475×10−02

4.2303×10−02

4.67×10−02

4.1

 

100

8.5100×10−03

3.0405×10−03

3.11×10−03

1.1

(0.01, 2, 1)

10

5.0499×10−02

4.4876×10−03

7.04×10−03

110.7

 

100

5.2245×10−03

7.4338×10−05

1.02×10−04

56.6

  1. In each row the summary statistics pertain to the parameter shown in bold, and are empirically determined from 1,000 simulated realizations. The CV value is the coefficient of variation expressed as a percentage