On ZLindley distribution: statistical properties and applications

Authors

  • Noureddine Saaidia
  • Thara Belhamra
  • Halim Zeghdoudi

DOI:

https://doi.org/10.54021/seesv5n1-153

Keywords:

Lindley distribution, moments, reliability analysis, simulation

Abstract

The modeling and analysis of lifetime data is critical in many areas, including actuarial science, management, engineering, medicin, physics, biology, hydrology, and computer science. Classical probability distributions have been used to manage data sets of varied sizes. However, considerable issues occur when real-world data does not fit into any of the classical or conventional probability models. Consequently, there arises a crucial requirement to enhance the flexibility of existing probability models by including the blending of two distributions or introducing additional parameters. This work introduces a ZLindley distribution with a single parameter. Both symmetric and left-skewed data can utilize the proposed model. We generate statistical features such as the mode, moments, quantile function, and moment-generating function to accurately represent the usefulness of the suggested distribution. We compute the parameter using the maximum likelihood estimation approach. A thorough simulation exercise evaluates the goodness-of-fit performance. We demonstrate the applicability and flexibility of the new recommended distribution by using a real dataset.

References

AZZALINI, A. A class of distributions which includes the normal ones. Scand. J. Stat, v. 12, n. 2, p. 171–178, 1985.

BEGHRICHE, A.; ZEGHDOUDI, H.; RAMAN, V.; CHOUIA, S. New polynomial exponential distribution: properties and applications. Statistics in Transition New Series, v. 23, n. 3, p. 95–112, 2022.

BOUCHAHED, L.; ZEGHDOUDI, H. A new and unified approach in generalizing the Lindley’s distribution with applications. Statistics, v. 61, 2018.

BOUHADJAR, M.; GEMEAY, A. M.; ALMETWALLY, E. M.; ZEGHDOUDI, H.; ALSHAWARBEH, E.; ALANAZI, T. A.; EL-RAOUF, M. M. A.; HUSSAM, E. The Power XLindley Distribution: Statistical Inference, Fuzzy Reliability, and COVID-19 Application. J. Funct. Spaces, v. 2022, p. 1–21, 2022.

BOURGUIGNON, M.; SILVA, R. B.; CORDEIRO, G. M. The Weibull- G Family of Probability Distributions. J. Data Sci, v. 12, n. 1, p. 53–68, 2014.

CHOUIA, S.; ZEGHDOUDI, H. The XLindley Distribution: Properties and Application.J. Stat. Theory Appl, v. 20, n. 2, p. 318, 2021.

DROST, F. Asymptotic for Generalized Chi-squared Goodness-of-fit Tests, Amsterdam: Centrefor Mathematics and Computer Sciences, CWI Tracs, v. 48. 1988.

EUGENE, N.; LEE, C.; FAMOYE, F. Beta-normal distribution and its applications. Commun. Stat. Methods, v. 31, n. 4, p. 497–512, 2002.

GREENWOOD, P. S.; NIKULIN, M. A guide to Chi-squared Testing. John Wiley and Sons, NewYork, 1996.

HSUAN, T. A.; ROBSON, D. S. The χ^2 Goodness-of-fit Tests with Moment Type Estimator. Communications in Statistics – Theory and Methods, v. 16, p. 1509-1519.1976.

HSUAN, T. A.; ROBSON, D. S. The χ2− Goodness-of-fit Tests with Moment Type Estimator.Communications in Statistics-Theory and Methods, v. 16, p. 1509-1519, 1976.

Krishnarani, S. D. On a power transformation of half-logistic distribution. J. Probab. Stat., v. 4, 2016.

LEE, E. T.; WANG, J. W. Statistical Methods for Survival Data Analysis. 3. ed. Wiley and Sons, New York, 2003.

MESSAADIA, H.; ZEGHDOUDI, H. Zeghdoudi distribution and its applications. International Journal of Computing Science and Mathematics, v. 9.1, 58-65.2018.

MIRVALIEV, M. An investigation of generalized chi-squared type statistics. Thesis (Doctorate) – Academy of Science of the Republic of Uzbekistan, Tashkent, 2001.

MURTHY, D. N. P.; XIE, M.; JIANG, R. Weibull Models. John Wiley & Sons, 2004.

NAWEL, K. et al. Modeling voltage real data set by a new version of Lindley distribution. IEEE Access, 2023.

NIKULIN, M. Chi-square Test For Continuous Distributions with Shift and Scale Parameters. Teor.Veroyatn.Primen, v. 18, n. 3, 559-568. 1973a.

NIKULIN, M. On a Chi-square Test For Continuous Distributions. Theory of Probability and Applications, v. 18, 638-639. 1973b.

RAO, K. C.; ROBSON, D. S. A chi-square statistic for goodness-of-fit tests within the exponential family.Communications in.Statistics, v. 3, p. 1139-1153.1974.

SEN, S.; MAITI, S. S.; CHANDRA, N. The xgamma distribution: Statistical properties and application. J. Mod. Appl. Stat. Methods, v. 15, n. 1, p. 774–788. 2016.

VAN DER VAART, A. W. Asymptotic Statistics. Cambridge Series in Statistics and probabilistic Mathematics. Cambridge: Cambridge University Press,1998.

VOINOV, V.; ALLOYAROVA, R.; PYA, N. Recent Achievemets in Modified Chi-squared Goodness-of-fit Testing.In:Statistical Models and Methods for Biomedical and Technical Systems. (Eds. F. Vonta, M. Nikulin, N. Limnios, C. Huber.). Birkhàuser, Boston, p. 241-258, 2008.

VOINOV, V.; PYA, N.; ALLOYAROVA, R. A Comparative Study of Some Modified Chi-squared Tests. Communi.in Stat.-Simul. AndComput, v. 38, n. 2, p. 355-367, 2009.

Published

2024-06-18

How to Cite

Saaidia, N., Belhamra, T., & Zeghdoudi, H. (2024). On ZLindley distribution: statistical properties and applications. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 3078–3097. https://doi.org/10.54021/seesv5n1-153