© H. R. Prodhani, R. Shanker. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
This study presents a three-parameter power quasi Sujatha distribution. Statistical properties including the survival function, hazard function, reverse hazard function, mean residual life function and stochastic ordering have been discussed. Moments of the proposed distribution have been obtained. The estimation of the parameters using the maximum likelihood method and maximum product spacing estimation has been explained and a simulation study has been presented to determine the efficiency of the maximum likelihood estimate of the parameters. The bootstrap confidence interval method has been used to estimate the confidence interval of the parameters. Finally, two examples of real lifetime datasets have been presented to demonstrate the applications of the proposed distribution. Also, the goodness of fit test shows a better fit compared to the three-parameter power Sujatha distribution, power quasi Lindley distribution, generalized gamma distribution, three-parameter Sujatha distribution and threeparameter generalized Lindley distribution.
KEYWORDS
quasi Sujatha distribution, statistical properties, maximum likelihood estimation, maximum product spacing estimation, applications
REFERENCES
Aderoju, S., Adeniyi, I., (2022). On Power Generalized Akash Distribution with Properties and Applications. Journal of Statistical Modeling and Analytics, Vol. 4(1), pp. 1–13.
Alkarni S., (2015). Power quasi-Lindley distribution. Properties and application. Asian Journal of Mathematics and Computer Research, Vol. 10(2), pp. 179–195.
Choulakian, V., Stephens, M. A., (2001). Goodness-of-Fit tests for the generalized Pareto distribution. Technometrices, Vol. 43, pp. 478–484.
Davison, A. C., Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge University Press.
Efron, B., Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC.
Ghitany, M.E., Atieh, B. and Nadarajah, S., (2008). Lindley distribution and its applications. Mathematics and Computer in Simulation, Vol. 78, pp. 493–506.
Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan N. and Al-Enezi, L. J., (2013). Power Lindley distribution and associated inference. Computational Statistics & Data Analysis, Vol. 64, pp. 20–33.
Lindley, D. V., (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society, Series B, Vol. 20(1), pp. 102–107.
Murthy, D. N. P, Xie, M. and Jiang, R., (2004), Weibull models, John Wily & Sons Inc., Hoboken.
Mussie, T., Shanker, R., (2018). A two parameter Sujatha distribution. Biometrics & Biostatistics International Journal, Vol. 7(3), pp. 188–197.
Nosakhare, E. and Festus, O., (2018). A three-parameter generalized Lindley distribution: Properties and Application. Statistica, Vol. 78(3), pp. 1–17.
Nwikpe, B. J., Iwok, I. A., (2020). A three-parameter Sujatha distribution with application. European Journal of Statistics and Probability, Vol. 8(3), pp. 22–34.
Picciotto R., (1970). Tensile fatigue characteristics of a sized polyester/viscose yarn and their effect on weaving performance, Master thesis, University of Raleigh, North Carolina State, USA.
Prodhani, H. R., Shanker, R., (2023). On some statistical properties and applications of three-parameter Sujatha distribution. Reliability: Theory & Applications, Vol. 18(3), pp. 514–527.
Prodhani, H. R., Shanker, R., (2024). A three-parameter power Sujatha distribution with properties and application. International Journal of Statistics and Reliability Engineering, Vol. 11(1), pp. 70–78.
Prodhani, H. R., Shanker, R., (2024). Power Pratibha distribution with properties and applications. International Journal of Statistics and Reliability Engineering, Vol. 11(2), pp. 217–226.
Shanker, R., Mishra, A., (2013). A quasi-Lindley distribution. African Journal of Mathematics and Computer Science Research, Vol. 6(4), pp. 64–71.
Shanker, R., (2016a). Sujatha distribution and its applications. Statistics in Transition New Series, Vol. 17(3), pp. 391–410.
Shanker, R., (2016b). A Quasi Sujatha distribution. International Journal of Probability and Statistics, Vol. 5(4), pp. 89–100.
Shanker, R., (2016c). Aradhana Distribution and Its applications. International Journal of Statistics and Applications, Vol. 6(1), pp. 23–34.
Shanker, R., Shukla, K. K., (2018). A two-parameter power Aradhana distribution with properties and application. Indian Journal of Industrial and Applied Mathematics, Vol. 9(2), pp. 210–220.
Shanker, R., Shukla, K. K and Sigh, A. P., (2018). A generalized Akash distribution. Biometrics & Biostatistics International Journal, Vol. 7(1), pp. 18–26.
Shanker, R., Shukla, K. K., (2019). A two-parameter power Sujatha distribution with properties and application. International Journal of Mathematics and Statistics, Vol. 20(3), pp. 11–22.
Shanker, R., (2023). Pratibha distribution with properties and application. Biometrics & Biostatistics International Journal, Vol. 12(5), pp. 136–142.
Stacy, E. W., (1962). A generalized gamma distribution. Annals of Mathematical Statistics, Vol. 33, pp. 1187–1192.
Shukla, K. K., (2018). Pranav distribution with properties and its applications. Biometrics & Biostatistics International Journal, Vol. 7(3), pp. 244–254.
Shukla, K. K., (2019). Power Pranav distribution and its applications to model lifetime data. Journal of applied quantitative methods, Vol. 14(2), pp. 1–13.
Shaked, M., Shanthikumar, J., (1994). Stochastic Orders and Their Applications. Academic Press, New York.