From: The beta Burr type X distribution properties with application
n | Parameter | Bias | RMSE |
---|---|---|---|
100 | \(\hat{\alpha }\) | 3.34 × 10−2 | 4.73 × 10−4 |
\(\hat{\beta }\) | −7.47 × 10−3 | 1.05 × 10−4 | |
\(\hat{\lambda }\) | −1.93 × 10−3 | 2.73 × 10−5 | |
\(\hat{\theta }\) | 2.09 × 10−4 | 2.95 × 10−6 | |
500 | \(\hat{\alpha }\) | 1.13 × 10−2 | 1.60 × 10−4 |
\(\hat{\beta }\) | −6.52 × 10−4 | 9.23 × 10−5 | |
\(\hat{\lambda }\) | −3.84 × 10−3 | 5.43 × 10−5 | |
\(\hat{\theta }\) | −8.10 × 10−7 | 1.13 × 10−8 | |
1000 | \(\hat{\alpha }\) | −1.63 × 10−2 | 2.31 × 10−4 |
\(\hat{\beta }\) | −9.48 × 10−3 | 1.34 × 10−4 | |
\(\hat{\lambda }\) | −2.12 × 10−4 | 3.01 × 10−6 | |
\(\hat{\theta }\) | 4.65 × 10−7 | 6.57 × 10−9 | |
1500 | \(\hat{\alpha }\) | −1.24 × 10−8 | 1.76 × 10−10 |
\(\hat{\beta }\) | 5.42 × 10−8 | 7.66 × 10−10 | |
\(\hat{\lambda }\) | 6.58 × 10−5 | 9.31 × 10−6 | |
\(\hat{\theta }\) | −1.13 × 10−9 | 1.60 × 10−11 |