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In this Paper, we have introduced a new version of new quasi lindley distribution known as the length-biased weighted new quasi lindley distribution (LBWNQLD). Length biased distribution is a special case of weighted distribution. The different structural properties of the newly proposed distribution are derived and the model parameters are estimated by using the method of maximum likelihood estimation and also the Fisher’s information matrix have been discussed. Finally, applications to real life two data sets are presented for illustration.


Weighted distribution New quasi lindley distribution Order Statistics Maximum likelihood estimation Reliability Analysis Entropies

Article Details

Author Biographies

Rashid A. Ganaie, Annamalai University

Department of Statistics

Ph.d Research Scholar

V. Rajagopalan, Annamalai University

Department of Statistics


How to Cite
Ganaie, R. A., & Rajagopalan, V. (2021). Length biased Weighted New Quasi Lindley Distribution: Statistical Properties and Applications. Pakistan Journal of Statistics and Operation Research, 17(1), 123-136.


  1. Abouammoh, A. M., Ahmed, R., & Khalique, A. (2000). On new renewal better than used classes of life distribution. Statistics and Probability Letters, 48, 189-194. DOI:
  2. Afaq, A., Ahmad, S. P., & Ahmed, A. (2016). Length-Biased weighted Lomax distribution: Statistical properties and applications. Pak.j.Stat.Oper.res, 12(2), 245-255. DOI:
  3. Cox, D. R. (1969). Some sampling problems in technology in New Development in Survey Sampling. Johnson, N. L. and Smith, H., Jr. (eds.) New York Wiley- Interscience, 506-527.
  4. Fisher, R. A. (1934). The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics, 6, 13 – 25. DOI:
  5. Ganaie, R. A., Rajagopalan, V., & Rather, A. A. (2019). A New Length Biased distribution With Applications. Science, Technology and Development, 8(8), 161-174.
  6. Ganaie, R. A., Rajagopalan, V., & Rather, A. A. (2020). On weighted two parameter quasi Shanker distribution with properties and its applications. International journal of statistics and reliability engineering, 7(1), 1-12.
  7. Hassan, A., Wani, S. A., & Para, B. A. (2018). On three Parameter Weighted Quasi Lindley Distribution: Properties and Applications. International journal of scientific research in mathematical and statistical sciences, 5(5), 210-224. DOI:
  8. Hassan, A., Dar, M. A., Peer, B. A., & Para, B. A. (2019). A new generalization of Pranav distribution using weighted technique. International journal of scientific research in mathematical and statistical sciences, 6(1), 25-32.
  9. Mudasir, S. & Ahmad, S. P. (2018). Characterization and estimation of length biased Nakagami distribution. Pak.j.stat.oper.res., 14(3), 697-715. DOI:
  10. Para, B. A. & Jan, T. R. (2018). On three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences. Applied Mathematics and Information Sciences Letters, 6 (1), 13-26. DOI:
  11. Patil, G. P. & Rao, C. R. (1978). Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families. Biometrics, 34(2), 179.doi:10.2307/2530008. DOI:
  12. Reyad, M. H., Hashish, M. A., Othman, A. S. & Allam, A. S. (2017). The length-biased weighted frechet distribution: properties and estimation. International journal of statistics and applied mathematics, 3(1), 189-200.
  13. Rao, C. R. (1965). On discrete distributions arising out of methods of ascertainment In: Patil, G.P.(eds) Classical and Contagious Discrete Distributions. Statistical Publishing Society, Calcutta, 320 – 332.
  14. Rather, A. A. & Subramanian, C. (2019). Length biased erlang truncated exponential distribution with lifetime data. Journal of information and computational science, 9(8), 340-355.
  15. Rather, A. A. & Ozel, G. (2020). The weighted power Lindley distribution with applications on the life time data. Pak.j.stat.oper.res., 16(2), 225-237. DOI:
  16. Shanker, R. & Ghebretsadik, A.H. (2013). A New Quasi Lindley distribution. International Journal of Statistics and Systems, 8(2), 143-156.
  17. Van Deusen, P.C. (1986). Fitting assumed distributions to horizontal point sample diameters. Forest Science, 32, 146-148.
  18. Warren, W. (1975). Statistical distributions in forestry and forest products research. In: Patil, G.P., Kotz, S. and Ord, J.K. (eds) Statistical Distributions in Scientific Work. D. Reidel, Dordrecht, The Netherlands, 2, 369-384.
  19. Xu, K., Xie, M., Tang, L.C. & Ho, S.L. (2003). Application of neural networks in forecasting engine systems reliability. Applied Soft Computing, 2 (4), 255-268. DOI:
  20. Zelen, M. (1974). Problems in cell kinetic and the early detection of disease, in Reliability and Biometry, F. Proschan & R. J. Sering, eds, SIAM, Philadelphia, 701-706.