Beta Exponentiated Modified Weibull Distribution: Properties and Application
Abstract
:1. Introduction
2. Beta Exponentiated Modified Weibull Distribution
2.1. Special Cases of the BEMW Distribution
2.1.1. Beta Exponentiated Weibull (BEW) Distribution
2.1.2. Beta Generalized Rayleigh (BGR) Distribution
2.1.3. Beta Modified Weibull (BMW) Distribution
2.1.4. Beta Rayleigh (BR) Distribution
2.1.5. Beta Exponentiated Exponential (BEE) Distribution
2.1.6. Beta Generalized Linear Failure Rate (BGLFR) Distribution
2.1.7. Exponentiated Modified Weibull (EMW) Distribution
3. Expansion of the Probability Distribution and Density Function
4. Statistical Properties
Moments
5. Order Statistics of the Beta Exponentiated Modified Weibull Distribution
6. Reliability Analysis
6.1. Survival Function
6.2. Hazard Function
7. Parameter Estimation
7.1. Maximum Likelihood Estimation
7.2. Least Squares Estimation
8. Application
9. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Length | Average | Minimum | Maximum | Median | Standard Deviation | ||
---|---|---|---|---|---|---|---|
40 | 6.2525 | 1.6 | 9.0 | 5.075 | 6.50 | 7.825 | 1.95553 |
Model | AIC | BIC | AICc | ||||||
---|---|---|---|---|---|---|---|---|---|
BEMWD | 2.6629 | 0.9664 | 2.9256 | 0.2769 | 1.6231 | 0.3785 | 24.99 | 35.13 | 27.54 |
(0.5594) | (2.0912) | (0.5068) | (7.7832) | (37.7734) | (23.1998) | ||||
EMWD | - | - | 26.9086 | 7.6903 | 15.1406 | 0.01399 | 28.69 | 35.44 | 29.83 |
(0.0916) | (15.0308) | (0.5086) | (742.7817) | ||||||
MWD | - | - | - | 0.1895 | 0.2810 | 4.0529 | 34.34 | 39.41 | 35.01 |
(7.3718) | (3.3962) | (2775.03) | |||||||
ED | - | - | - | - | - | 0.1817 | 30.56 | 32.25 | 30.66 |
(8.0248) |
Model | AIC | BIC | AICc | ||||||
---|---|---|---|---|---|---|---|---|---|
BEMWD | 1.4268 | 1.3079 | 1.500 | 0.9999 | 1.9999 | 1.8999 | 18.34 | 28.47 | 20.89 |
(3.7841) | (0.3475) | (0.0003) | (0.0019) | (0.0119) | (0.0115) | ||||
EMWD | - | - | 1.5129 | 0.9689 | 1.8378 | 1.7407 | 34.34 | 41.10 | 35.48 |
(0.0006) | (0.0483) | (0.1911) | (0.2035) | ||||||
MWD | - | - | - | 0.9893 | 1.9366 | 1.8392 | 32.34 | 37.41 | 33.01 |
(0.0179) | (0.0920) | (0.0925) | |||||||
ED | - | - | - | - | - | 0.1353 | 24.56 | 26.25 | 24.66 |
(9.8036) |
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Shahzad, M.N.; Ullah, E.; Hussanan, A. Beta Exponentiated Modified Weibull Distribution: Properties and Application. Symmetry 2019, 11, 781. https://doi.org/10.3390/sym11060781
Shahzad MN, Ullah E, Hussanan A. Beta Exponentiated Modified Weibull Distribution: Properties and Application. Symmetry. 2019; 11(6):781. https://doi.org/10.3390/sym11060781
Chicago/Turabian StyleShahzad, Mirza Naveed, Ehsan Ullah, and Abid Hussanan. 2019. "Beta Exponentiated Modified Weibull Distribution: Properties and Application" Symmetry 11, no. 6: 781. https://doi.org/10.3390/sym11060781