A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications
Abstract
:1. Introduction
2. The OLLBSP Distribution
3. Inference and Estimation
4. Structural Properties
4.1. Linear Representation
4.2. Moments
5. The LOLLBSP Regression Model with Censored Data
6. Applications
6.1. Data Set 1: Breaking Stress of Carbon Fibres (In Gba)
6.2. Data Set 2: Ambient Temperature Data
7. Concluding Remarks
Author Contributions
Conflicts of Interest
References
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Sample Size | Parameter | Mean | Bias | MSE | |
---|---|---|---|---|---|
a | 2.7479 | 0.2479 | 0.5496 | ||
b | 1.2505 | −0.2495 | 0.2038 | ||
2.1559 | 0.1559 | 0.3803 | |||
1.4741 | 0.7241 | 1.4878 | |||
a | 2.7228 | 0.2228 | 0.5063 | ||
b | 1.3640 | −0.1360 | 0.1263 | ||
2.1356 | 0.1356 | 0.3608 | |||
Setup 1 | 1.1648 | 0.4148 | 0.7094 | ||
a | 2.6960 | 0.1960 | 0.4276 | ||
b | 1.4476 | −0.0524 | 0.0709 | ||
2.1111 | 0.1111 | 0.3104 | |||
0.9102 | 0.1602 | 0.3297 | |||
a | 2.6507 | 0.1507 | 0.3695 | ||
b | 1.4466 | −0.0534 | 0.0551 | ||
2.1084 | 0.1084 | 0.2584 | |||
0.9014 | 0.1514 | 0.2706 | |||
a | 0.7487 | −0.0013 | 0.2457 | ||
b | 3.0076 | 0.0076 | 0.4509 | ||
0.9691 | −0.0309 | 0.5599 | |||
2.1168 | 0.1168 | 1.4317 | |||
a | 0.7544 | 0.0044 | 0.1970 | ||
b | 2.9874 | −0.0126 | 0.3606 | ||
0.9754 | −0.0246 | 0.4350 | |||
Setup 2 | 2.1233 | 0.1233 | 1.3254 | ||
a | 0.7616 | 0.0116 | 0.0920 | ||
b | 2.9967 | −0.0033 | 0.3039 | ||
0.9928 | −0.0072 | 0.1912 | |||
2.1087 | 0.1087 | 1.1643 | |||
a | 0.7525 | 0.0025 | 0.0447 | ||
b | 2.9996 | −0.0004 | 0.2216 | ||
0.9853 | −0.0147 | 0.0876 | |||
2.0678 | 0.0678 | 0.8310 | |||
a | 1.5922 | 0.0922 | 0.7011 | ||
b | 3.0035 | 0.0035 | 0.5183 | ||
0.8068 | 0.0568 | 0.2529 | |||
1.3356 | 0.0856 | 0.4881 | |||
a | 1.5724 | 0.0724 | 0.4521 | ||
b | 3.0179 | 0.0179 | 0.2984 | ||
0.7955 | 0.0455 | 0.1701 | |||
Setup 3 | 1.2694 | 0.0194 | 0.2892 | ||
a | 1.5195 | 0.0195 | 0.2394 | ||
b | 3.0461 | 0.0461 | 0.1839 | ||
0.7637 | 0.0137 | 0.0910 | |||
1.2415 | −0.0085 | 0.1530 | |||
a | 1.5229 | 0.0229 | 0.1487 | ||
b | 3.0199 | 0.0199 | 0.1186 | ||
0.7651 | 0.0151 | 0.0573 | |||
1.2527 | 0.0027 | 0.1108 |
Model | a | b | ||||
---|---|---|---|---|---|---|
BS | 0.4621 | 2.3661 | 0.2978 | 1.6181 | ||
(0.0326) | (0.1064) | |||||
MOEBS | 2.8026 | 0.0250 | 9909.4580 | 0.0798 | 0.5580 | |
(0.4486) | (0.0078) | (435.3655) | ||||
OLLBS | 217.3455 | 2.4788 | 530.5732 | 0.2461 | 1.2847 | |
(0.1095) | (0.0557) | (0.1012) | ||||
OLLBSP | 0.3173 | 1.2653 | 0.3993 | 4.7372 | 0.0711 | 0.3945 |
(0.0977) | (0.3080) | (0.1697) | (1.6564) | |||
BBS | 97.3898 | 0.0075 | 629.2049 | 466.4159 | 0.1040 | 0.5363 |
(24.6425) | (0.0011) | (236.0238) | ( 203.7381) | |||
KWBS | 12.9322 | 0.0054 | 26.0008 | 2.1588 | 0.1486 | 0.7541 |
(1.6490) | (0.0006) | (5.2036) | (0.7928) | |||
EGBS | 1.7685 | 69.7519 | 105.9274 | 0.3928 | 0.1603 | 0.8570 |
(0.0736) | (0.0859) | (0.4150) | (0.0726) |
Statistic | |||
Model | AIC | CAIC | BIC |
LOLLBSP | 61.1 | 66.0 | 68.2 |
LMcBS | 76.7 | 67.7 | 68.9 |
LBBS | 73.2 | 78.2 | 80.3 |
LBS | 66.4 | 67.6 | 69.9 |
Model | a | |||||
---|---|---|---|---|---|---|
LOLLBSP | 1.5548 | 0.1062 | 0.1031 | 3.9382 | 6.6303 | −0.02936 |
(0.9542) | (0.01876) | (0.005682) | (1.06512) | (0.2890) | (0.001231) | |
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Cordeiro, G.M.; De Lima, M.D.C.S.; Ortega, E.M.M.; Suzuki, A.K. A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications. Stats 2018, 1, 32-47. https://doi.org/10.3390/stats1010004
Cordeiro GM, De Lima MDCS, Ortega EMM, Suzuki AK. A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications. Stats. 2018; 1(1):32-47. https://doi.org/10.3390/stats1010004
Chicago/Turabian StyleCordeiro, Gauss Moutinho, Maria Do Carmo Soares De Lima, Edwin Moisés Marcos Ortega, and Adriano Kamimura Suzuki. 2018. "A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications" Stats 1, no. 1: 32-47. https://doi.org/10.3390/stats1010004