.svg){kind=logo}
WEIBULL-SUJATHA DISTRIBUTION WITH APPLICATION
Keywords:
Weibull distribution, Weibull-Sujatha distribution, Rényi entropy, Shannon entropy, maximum likelihood methodDOI:
https://doi.org/10.17654/0972361725070Abstract
This paper proposes a new distribution that represents a new extension of the Weibull distribution. The paper initiates studying the behavior of the new distribution function and comparing it with the behavior of the classical Weibull distribution function. The shapes of the probability density function are studied, and the properties of this distribution are examined with bearing in mind that the quantile and median, the moments, moment generating function, characteristic function, Rényi and Shannon entropy and Bonferroni and Lorenz curves are all inclusive. The maximum likelihood method is used for the sake of estimating the proposed distribution parameters and the results of simulation are expounded. Two applied instances are highlighted to elucidate the estimation efficiency, and the outstanding privileges of the proposed distribution over a group of classical distributions are brought to the forefront.
Received: August 7, 2025
Revised: August 25, 2025
Accepted: October 6, 2025
References
[1] A. M. Abouammoh, A. M. Alshangiti and I. E. Ragab, A new generalized Lindley distribution, J. Stat. Comput. Simul. 85 (2015), 3662-3678.
[2] S. H. Alkarni, Extended power Lindley distribution: a new statistical model for non monotone survival data, European Journal of Statistics and Probability 3(3) (2015), 19-34.
[3] B. Al-Zahrani, Goodness-of-fit for the Topp-Leone distribution with unknown parameters, Appl. Math. Sci. 6(128) (2012), 6355-6363.
[4] A. Asgharzadeh, S. Nadarajah and F. Sharafi, Weibull Lindley distribution, REVSTAT 16 (2018), 87-113.
[5] H. S. Bakouch, B. M. Al Zahrani and A. A. Al Shomrani, An extended Lindley distribution, J. Korean Statist. Soc. 41(1) (2012), 75-85.
[6] C. E. Bonferroni, Elmenti di statisticagenerale, LibreriaSeber, Firenze, 1930.
[7] S. Chouia and H. Zeghdoudi, The XLindley distribution: properties and application, J. Stat. Theory Appl. 20(2) (2021), 318-327.
[8] G. M. Cordeiro, A. Z. Afify, H. M. Yousof, S. Cakmakyapan and G. Ozel, The Lindley Weibull distribution: properties and applications, Anais da Academia Brasileira de Ciências 90(3) (2018), 2579-2598.
[9] F. Y. Eissa and C. D. Sonar, Generalization of power Lindley distribution: properties and applications, Statistics, Optimization and Information Computing 12 (2024), 1019-1041.
[10] I. Elbatal, F. Merovi and M. A. Elgarhy, New generalized Lindley distribution, Mathematical Theory and Modelling 3(13) (2013), 30-37.
[11] M. E. Ghitany, D. K. Al-Mutairi, N. Balakrishnan and L. J. Al-Enezi, Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64 (2013), 20-33.
[12] N. B. John and I. I. Aniefiok, A three-parameter Sujatha distribution with application, European Journal of Statistics and Probability 8(3) (2020), 22-34.
[13] C. D. Lai, M. Xie and D. N. P. Murthy, A modified Weibull distribution, IEEE Trans. Reliab. 52 (2003), 33-37.
[14] D. V. Lindley, Fiducial distributions and Bayes’ theorem, J. Roy. Statist. Soc. Ser. B 20 (1958), 102-107.
[15] G. Liyanage and M. Parai, The generalized power Lindley distribution with its applications, Asian Journal of Mathematics and Applications 73 (2014), 331-359.
[16] M. O. Lorenz, Methods of measuring the concentration of wealth, Quarterly Publications of the American Statistical Association 9 (1905), 209-219.
[17] P. Marthin and G. S. Rao, Generalized Weibull-Lindley (GWL) distribution in modeling lifetime data, Journal of Mathematics 2020 (2020), 1-15.
[18] T. Mussie and R. Shanker, A two-parameter Sujatha distribution, Biometrics and Biostatistics International Journal 7(3) (2018), 188-197.
[19] B. O. Oluyede, M. Fedelis and H. Shujiao, The log-generalized Lindley-Weibull distribution with applications, Journal of Data Science 13(2) (2015), 281-310.
[20] C. L. Ramos et al., Evaluation of stress tolerance and fermentative behavior of indigenous Saccharomyces cerevisiae, Braz. J. Microbiol. 44(3) (2013), 935-944.
[21] J. W. S. Rayleigh, On the resultant of a large number of vibrations of the same pitch and of arbitrary phase, Philosophical Magazine, 5th Series, Vol. 10, 1880, pp. 73-78.
[22] A. Rényi, On measures of entropy and information, J. Neyman, ed., 4th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, Vol. 1, 1961, pp. 574-561.
[23] R. Shanke and K. K. Shukla, On two-parameter Akash distribution, Biometrics and Biostatistics International Journal 6 (2017), 416-425.
[24] R. Shanker, Akash distribution and its applications, International Journal of Probability and Statistics 4(3) (2015), 65-75.
[25] R. Shanker, Sujatha distribution and its applications, Statistics in Transition, New Series 17(3) (2016), 391-410.
[26] R. Shanker and A. Mishra, A two-parameter Poisson-Lindley distribution, International Journal of Statistics and Systems 9(1) (2014), 79-85.
[27] R. Shanker and A. Mishra, A quasi Lindley distribution, African Journal of Mathematics and Computer Science Research 6(4) (2013), 64-71.
[28] C. E. Shannon, A mathematical theory of communication, The Bell System Technical Journal 27 (1948), 379-423.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
