# A New Weighted Topp-Leone Family of Distributions

### Abstract

Based on T-X transform due to Alzaatreh et al. (2013), we propose the new weighted Topp-Leone (NWTL-Π) continuous statistical distributions with two extra shpae parameters .Then we study some basic mathematical properties. Then we study Uniform model as member of the new class with more details. Using a simulation study, we compared some methods of estimation. Finally we analyzed and used lifetime and failure time real data sets to illustrate the purposes.### References

Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S., & Shahbaz, M. Q. (2016). Topp–Leone family of distributions: some properties and application.Pakistan Journal of Statistics and Operation Research,12(3), 443-451.

Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain ”goodness of fit” criteria based on stochastic processes. The annals of mathematical statistics, 193-212.

Alizadeh, M., Lak, F., Rasekhi, M., Ramires, T. G., Yousof, H. M., & Altun, E. (2018). The odd log-logistic Topp–Leone G family of distributions: heteroscedastic regression models and applications. Computational Statistics, 33(3), 1217-1244.

Alzaatreh, A., Lee, C., & Famoye, F. (2013). A new method for generating families of continuous distributions.Metron, 71(1), 63-79

Balakrishnan, N. (1985). Order statistics from the half logistic distribution. Journal of Statistical Computation and Simulation, 20(4), 287-309.

Brito, E., Cordeiro, G. M., Yousof, H. M., Alizadeh, M., & Silva, G. O. (2017). The Topp–Leone odd log-logistic family of

distributions.Journal of Statistical Computation and Simulation, 87(15), 3040-3058.

Cheng RCH, Amin NAK (1979) Maximum product-of-spacings estimation with applications to the lognormal distribution. Technical Report, Department of Mathematics, University of Wales

Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J R Stat Soc B3:394-403.

Choi, K. and Bulgren, W. (1968). An estimation procedure for mixtures of distributions. Journal of the Royal Statistical Society. Series B (Methodological), 444-460.

Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of statistical computation and simulation, 81(7), 883-898.

Corless, R. M., Gonnet, G. H., Hare, D. E., Jeffrey, D. J., & Knuth, D. E. (1996). On the LambertW function. Advances in

Computational mathematics, 5(1), 329-359.

Dey, S., Mazucheli, J., & Nadarajah, S. (2017). Kumaraswamy distribution: different methods of estimation. Computational and Applied Mathematics, 1-18.

Ghitany, M. E., Atieh, B., & Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and computers in simulation, 78(4), 493-506.

Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., & Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference. Computational Statistics & Data Analysis, 64, 20-33.

Gleaton, J. U., & Lynch, J. D. (2006). Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4(1), 51-64.

Gradshteyn, I. S. and Ryzhik, I. M. (2007), Table of Integrals, Series, and Products,7 edn, Academic Press, New York.

Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.

Gupta, R. D., & Kundu, D. (2009). A new class of weighted exponential distributions. Statistics, 43(6), 621-634.

Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of hydrology, 46(1-2), 79-88.

Jones, M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1), 1-43.

Leadbetter, M. R., Lindgren, G., & Rootz´en, H. (2012). Extremes and related properties of random sequences and processes. Springer Science & Business Media.

Murthy, D. P., Xie, M., & Jiang, R. (2004). Weibull models Vol. 505. John Wiley & Sons.

Nadarajah, S., Bakouch, H. S., & Tahmasbi, R. (2011). A generalized Lindley distribution.Sankhya B, 73(2), 331-359.

Ozel, G., Alizadeh, M., Cakmakyapan, S., Hamedani, G. G., Ortega, E. M., & Cancho, V. G. (2017). The odd log-logistic Lindley Poisson model for lifetime data. Communications in Statistics-Simulation and Computation, 46(8), 6513-6537.

Ranjbar, V., Alizadeh, M., & Altun, E. (2019). Extended Generalized Lindley distribution: properties and applications. Journal of Mathematical Extension, 13, 117-142.

R´enyi, A. (1961). On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 547-561.

Reyad, H., Alizadeh, M., Jamal, F., & Othman, S. (2018). The Topp Leone odd Lindley-G family of distributions: properties and applications. Journal of Statistics and Management Systems,21(7), 1273-1297.

Rezaei, S., Sadr, B. B., Alizadeh, M., & Nadarajah, S. (2017). Topp–Leone generated family of distributions: Properties and applications. Communications in Statistics-Theory and Methods, 46(6), 2893-2909.

Sangsanit, Y., & Bodhisuwan, W. (2016). The Topp-Leone generator of distributions: properties and inferences. Songklanakarin Journal of Science & Technology, 38(5).

Shannon, C.E. (1951). Prediction and entropy of printed English. The Bell System Technical Journal, 30, 50-64.

Swain, J. J., Venkatraman, S., and Wilson, J. R. (1988). Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29, 271- 297.

Topp, C. W., & Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269), 209-219.

Yousof, H. M., Alizadeh, M., Jahanshahi, S. M. A., Ramires, T. G., Ghosh, I., & Hamedani, G. G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications. Journal of Data Science,15(4), 723-740.

*Statistics, Optimization & Information Computing*,

*11*(3), 615-628. https://doi.org/10.19139/soic-2310-5070-1514

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