DOI QR코드

DOI QR Code

A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation

  • Ibrahim, Mohamed (Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University) ;
  • Yadav, Abhimanyu Singh (Department of statistics, Central University of Rajasthan) ;
  • Yousof, Haitham M. (Department of Statistics, Mathematics and Insurance, Benha University) ;
  • Goual, Hafida (Laboratory of Probability and Statistics University of Badji Mokhtar) ;
  • Hamedani, G.G. (Department of Mathematics, Statistics and Computer Science, Marquette University)
  • 투고 : 2019.03.29
  • 심사 : 2019.07.26
  • 발행 : 2019.09.30

초록

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

키워드

참고문헌

  1. Alizadeh M, Rasekhi M, Yousof HM, and Hamedani GG (2017). The transmuted Weibull G family of distributions, Hacettepe Journal of Mathematics and Statistics, 47, 1-20.
  2. Alizadeh M, Yousof HM, Afify AZ, Cordeiro GM, and Mansoor M (2016). The complementary generalized transmuted Poisson-G family of distributions, Austrian Journal of Statistics, 47, 51-71.
  3. Badar MG and Priest AM (1982). Statistical aspects of fiber and bundle strength in hybrid composites. In Hayashi, T., Kawata, K. and Umekawa, S. (eds), Progress in Science and Engineering Composites (pp. 1129-1136), ICCM-IV, Tokyo.
  4. Casella G and Berger RL (2002). Statistical Inference, Cengage Learning India Private Limited, Delhi.
  5. Deniz E and Ojeda E (2011). The discrete Lindley distribution-properties and applications, Journal of Statistical Computation and Simulation, 81, 1405-1416. https://doi.org/10.1080/00949655.2010.487825
  6. Ghitany ME, Al-Mutairi DK, and Nadarajah S (2008a). Zero-truncated Poisson-Lindley distribution and its application, Mathematics and Computers in Simulation, 79, 279-287. https://doi.org/10.1016/j.matcom.2007.11.021
  7. Ghitany ME, Atieh B, and Nadarajah S (2008b). Lindley distribution and its application, Mathematics and Computers in Simulation, 78, 493-506. https://doi.org/10.1016/j.matcom.2007.06.007
  8. Ghitany ME, Alqallaf F, Al-Mutairi DK, and Husain HA (2011). A two-parameter weighted Lindley distribution and its applications to survival data, Mathematics and Computers in Simulation,81, 1190-1201. https://doi.org/10.1016/j.matcom.2010.11.005
  9. Glanzel W (1987). A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75-84.
  10. Glanzel W (1990). Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21, 613-618. https://doi.org/10.1080/02331889008802273
  11. GlanzelWand Hamedani GG (2001). Characterizations of univariate continuous distributions, Studia Scientiarum Mathematicarum Hungarica, 37, 83-118. https://doi.org/10.1556/SScMath.37.2001.1-2.5
  12. Gross J and Clark VA (1975). Survival Distributions: Reliability Applications in the Biometrical Sciences, John Wiley, New York.
  13. Hamedani GG (2013). On certain generalized gamma convolution distributions II (Technical report, No.484), MSCS, Marquette University.
  14. Hamedani GG, Altun E, Korkmaz MC, Yousof HM, and Butt NS (2018a). A new extended G family of continuous distributions with mathematical properties, characterizations and regression modeling, Pakistan Journal of Statistics and Operation Research, 14, 737-758. https://doi.org/10.18187/pjsor.v14i3.2484
  15. Hamedani GG, Yousof HM, Rasekhi M, Alizadeh M, and Najibi SM (2018b). Type I general exponential class of distributions, Pakistan Journal of Statistics and Operation Research, 14, 39-55. https://doi.org/10.18187/pjsor.v14i1.2193
  16. Lindley DV (1958). Fiducial distributions and Bayes' theorem, Journal of the Royal Statistical Society. Series B (Methodological), 102-107.
  17. MacDonald PDM (1971). Comment on an estimation procedure for mixtures of distributions by Choi and Bulgren, Journal of the Royal Statistical Society. Series B, 33, 326-329.
  18. Nadarajah S, Bakouch HS, and Tahmasbi R (2011). A generalized Lindley distribution, Sankhya B, 73, 331-359. https://doi.org/10.1007/s13571-011-0025-9
  19. Nikulin MS (1973). Chi-square test for continuous distribution with shift and scale parameters, Theory of Probability and its Applications, 19, 559-568.
  20. Pearson KFRS (1900). On the criterion that a given system of deviation from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50, 157-175. https://doi.org/10.1080/14786440009463897
  21. Rao KC and Robson DS (1974). A chi-square statistic for goodness-of-fit for tests within the exponential family, Communications in Statistics, 3, 1139-1153.
  22. Rezaei S, Sadr BB, Alizadeh M, and Nadarajah S (2017). Topp-Leone generated family of distributions: Properties and applications, Communications in Statistics-Theory and Methods, 46, 2893-2909. https://doi.org/10.1080/03610926.2015.1053935
  23. Swain JJ, Venkatraman S, and Wilson JR (1988). Least squares estimation of distribution functions in Johnson's translation system, Journal of Statistical Computation and Simulation, 29, 271-297 https://doi.org/10.1080/00949658808811068
  24. Voinov V, Alloyarova R, and Pya N (2008). Recent achievements in modified chi-squared goodness-of-fit testing, In Vonta, F., Nikulin, M., Limnios, N., and Huber, C. (Eds), Statistical Models and Methods for Biomedical and Technical Systems (pp. 245-262), Birkhauser, Boston.