# Topp-Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data
## Appendix A  
The second order partial derivatives of the log likelihood function of \(TLMW\) distribution with respect to \(\alpha\), \(\beta\), \(\theta\), \(\lambda\) are given by:  
Figure 28: ACF test plots for parameters of \(TLMW\) model for single carbon fibers. * _[PERSON] et al. (2022)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data. _Mathematics_**2022**, _10_, 1565. [CrossRef]
* _[PERSON] and [PERSON] (2019)_ [PERSON]; [PERSON] [PERSON] Exponentiated Weibull-Weibull Distribution: Statistical Properties and Applications. _Gazi J. Sci._**2019**, _32_, 616-635. * _[PERSON] et al. (2003)_ [PERSON]; [PERSON]; [PERSON]. A modified Weibull distribution. _IEEE Trans. Reliab._**2003**, _52_, 33-37. [CrossRef]
* _[PERSON] and [PERSON] Parameter estimation for a modified Weibull distribution, for progressively type-II censored samples. _IEEE Trans. Reliab._**2003**, _54_, 374-380. [CrossRef]
* _[PERSON] and [PERSON] (2009)_ [PERSON]; [PERSON] [PERSON] Modified Weibull distribution. _Appl. Sci._**2009**, _11_, 123-136. * _[PERSON] et al. (2008)_ [PERSON]; [PERSON]; [PERSON] A generalized modified Weibull distribution for lifetime modeling. _Comput. Stat. Data Anal._**2008**, _53_, 450-462. [CrossRef]
* _[PERSON] et al. (2010)_ [PERSON]; [PERSON]; [PERSON] The beta modified Weibull distribution. _Lifetime Data Anal._**2010**, _16_, 409-430 [CrossRef]
* _[PERSON] and [PERSON] (2013)_ [PERSON]; [PERSON] Exponentiated modified Weibull extension distribution. _Reliab. Eng. Syst. Saf._**2013**, _112_, 137-144. [CrossRef]
* _[PERSON] et al. (2013)_ [PERSON]; [PERSON] A new modified Weibull distribution. _Reliab. Eng. Syst. Saf._**2013**, _111_, 164-170. [CrossRef]
* _[PERSON] (2013)_ [PERSON]; [PERSON] Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. _Eur. J. Pure Appl. Math._**2013**, \(6\), 66-86. * _[PERSON] et al. (2013)_ [PERSON]; [PERSON] [PERSON] The McDonald modified Weibull distribution: Properties and applications. _arXiv_**2013**, arXiv:1309.2961. * _[PERSON] et al. (2014)_ [PERSON]; [PERSON]; [PERSON] The Kumaraswamy modified Weibull distribution: Theory and applications. _J. Stat. Comput. Simul._**2014**, _84_, 1387-1411. [CrossRef]
* _[PERSON] et al. (2015)_ [PERSON]; [PERSON]; [PERSON], T. A new class of generalized modified Weibull distributions with applications. _Austrian J. Stat._**2015**, _44_, 45-68. [CrossRef]
* _[PERSON] et al. (2017)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] The Burr XII modified Weibull distribution: Model, Properties and Applications. _Electron. J. Appl. Stat. Anal._**2017**, _10_, 118-145. * _[PERSON] et al. (2018)_ [PERSON]; [PERSON];[PERSON]; [PERSON] [PERSON] Anew generalized log-logistic and modified Weibull distribution with applications. _Int. J. Stat. Probab._**2018**, \(7\), 72-93. [CrossRef]
* _[PERSON] et al. (2019)_ [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A new extended Weibull model for lifetime data. _J. Appl. Probab._**2019**, \(4\), 57-73. * _[PERSON] et al. (2019)_ [PERSON]; [PERSON]; [PERSON] Beta Exponentiated Modified Weibull Distribution: Properties and Application. _Symmetry_**2019**, _11_, 781. [CrossRef]
* _[PERSON] et al. (2022)_ [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] Statistical Analysis of COVID-19 Data in Kingdom of Saudi Arabia Using: Sine Modified Weibull Model. _JP J. Biostat._**2022**, _20_, 11-26. [CrossRef]
* _[PERSON] and Leone (2016)_ [PERSON]; [PERSON] A family of J-shaped frequency functions. _J. Am. Stat. Assoc._**1955**, _50_, 209-219. [CrossRef]
* _[PERSON] et al. (2016)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Topp-Leone Family of Distributions: SomeProperties and Application. _Pak. J. Stat. Oper. Res._**2016**, _12_, 443. [CrossRef]
* _[PERSON] et al. (2019)_ [PERSON]; [PERSON]; [PERSON] Type II generalized Topp-Leone family of distributions: Properties and applications. _J.