A Weighted Exponentiated class of Distributions:Properties with Applications for Modelling Reliability Data
Keywords:
Exp-G family; Lindley distribution; Moment; Quantile; Simulation
Abstract
lIn this study, we suggest the weighted Exp-G (WExp-G) continuous distributions as a novel class of continuous distributions with an additional shape parameter. Then we study the basic mathematical properties. We study Lindley and XGamma special cases. This model is exible for modelling right skew data sets. The hazard rate of this model is decraesing, increasing and bathtub shape. By performing a simulation analysis, we compared different common methods of estimation. Finally we analyzed and used lifetime, failure time and stress real data sets to illustrate the purposes. This model is perfrom better than other two-parameter distribution.References
References
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[21] Rao, M., Chen, Y., Vemuri, B. C., Wang, F. (2004). Cumulative residual entropy: a new
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[22] Sen, S., Maiti, S. S., Chandra, N. (2016). The xgamma distribution: statistical properties
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Properties and Applications. Statistics, Optimization Information Computing.
https://doi.org/10.19139/soic-2310-5070-1210
[24] 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.
[25] Swain, J. J., Venkatraman, S., and Wilson, J. R. (1988). Least-squares estimation of dis-
tribution functions in johnson's translation system. Journal of Statistical Computation and
Simulation, 29, 271- 297.
[1] Alexander, C., Cordeiro, G. M., Ortega, E. M., Sarabia, J. M. (2012). Generalized beta-
generated distributions. Computational Statistics Data Analysis, 56(6), 1880-1897.
[2] Alizadeh, M., K MirMostafaee, S. M. T., Altun, E., Ozel, G., Khan Ahmadi, M. (2017).
The odd log-logistic marshall-olkin power lindley distribution: Properties and applications.
Journal of Statistics and Management Systems, 20(6), 1065-1093.
[3] Alizadeh, M., Altun, E., A fy, A. Z., Gamze, O. Z. E. L. (2018). The extended oddWeibull-
G family: properties and applications. Communications Faculty of Sciences University of
Ankara Series A1 Mathematics and Statistics, 68(1), 161-186.
[4] Alizadeh, M., Afshari, M., Hosseini, B., Ramires, T. G. (2018). Extended exp-G family
of distributions: Properties, applications and simulation.Communications in Statistics-
Simulation and Computation, 1-16.
[5] Alizadeh, M., Emadi, M., Doostparast, M. (2019). A new two-parameter lifetime distribu-
tion: properties, applications and different method of estimations. Statistics, Optimization
Information Computing, 7(2), 291-310.
[6] Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S., Shahbaz, M. Q. (2016). ToppLeone
family of distributions: some properties and application.Pakistan Journal of Statistics and
Operation Research,12(3), 443-451.
[7] Belzunce, F., Navarro, J., Ruiz, J. M., Aguila, Y. D. (2004). Some results on residual
entropy function. Metrika, 59(2), 147-161.
[8] Choi, K. and Bulgren, W. (1968). An estimation procedure for mixtures of distributions.
Journal of the Royal Statistical Society. Series B (Methodological), 444-460.
[9] Cordeiro, G. M., de Castro, M. (2011). A new family of generalized distributions. Journal
of statistical computation and simulation, 81(7), 883-898.
[10] Cordeiro, G. M., Ortega, E. M., da Cunha, D. C. (2013). The exponentiated generalized
class of distributions. Journal of Data Science, 11(1), 1-27.
[11] Cordeiro, G. M., Lima, M. D. C. S., Cysneiros, A. H., Pascoa, M. A., Pescim, R. R.,
Ortega, E. M. (2016). An extended Birnbaum-Saunders distribution: Theory, estimation,
and applications. Communications in Statistics-Theory and Methods, 45(8), 2268-2297.
[12] Ghitany, M. E., Atieh, B., Nadarajah, S. (2008). Lindley distribution and its application.
Mathematics and computers in simulation, 78(4), 493-506.
[13] 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.
[14] Gupta, R. C., Gupta, P. L., Gupta, R. D. (1998). Modelling failure time data by Lehman
alternatives. Communications in Statistics-Theory and methods, 27(4), 887-904.
[15] Gupta, R. D., Kundu, D. (1999). Theory methods: Generalized exponential distributions.
Australian New Zealand Journal of Statistics, 41(2), 173-188.
[16] Jones, M. C. (2004). Families of distributions arising from distributions of order statistics.
Test, 13(1), 1-43.
[17] Leadbetter, M. R., Lindgren, G., Rootzn, H. (2012). Extremes and related properties of
random sequences and processes. Springer Science Business Media.
[18] Lehmann, E. L. (1953). The power of rank tests. The Annals of Mathematical Statistics,
23-43.
[19] Murthy, D. P., Xie, M., Jiang, R. (2004). Weibull models Vol. 505. John Wiley Sons.
[20] Nadarajah, S., Bakouch, H. S., Tahmasbi, R. (2011). A generalized Lindley distribu-
tion.Sankhya B, 73(2), 331-359.
[21] Rao, M., Chen, Y., Vemuri, B. C., Wang, F. (2004). Cumulative residual entropy: a new
measure of information. IEEE transactions on Information Theory, 50(6), 1220-1228.
[22] Sen, S., Maiti, S. S., Chandra, N. (2016). The xgamma distribution: statistical properties
and application. Journal of Modern Applied Statistical Methods, 15(1), 38.
[23] Shaheed, G. (2021). A New Two-parameter Modi ed Half-logistic Distribution:
Properties and Applications. Statistics, Optimization Information Computing.
https://doi.org/10.19139/soic-2310-5070-1210
[24] 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.
[25] Swain, J. J., Venkatraman, S., and Wilson, J. R. (1988). Least-squares estimation of dis-
tribution functions in johnson's translation system. Journal of Statistical Computation and
Simulation, 29, 271- 297.
Published
2025-01-19
How to Cite
Shaheed, G. (2025). A Weighted Exponentiated class of Distributions:Properties with Applications for Modelling Reliability Data. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-1858
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