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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 1

Modified-Lindley distribution and its applications to the real data

Coşkun Kuş(SELÇUK ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ)0000-0002-7176-0176
Mustafa Çağatay Korkmaz(ARTVİN ÇORUH ÜNİVERSİTESİ)0000-0003-3302-0705
İsmail Kınacı(SELÇUK ÜNİVERSİTESİ, FEN FAKÜLTESİ)0000-0002-0992-4133
Kadir Karakaya(SELÇUK ÜNİVERSİTESİ, FEN FAKÜLTESİ)0000-0002-0781-3587
Yunus Akdoğan(SELÇUK ÜNİVERSİTESİ, FEN FAKÜLTESİ)0000-0003-3520-7493
Sayfa
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Yayın Tarihi
2022-03-30
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The distribution modeling analyses are provided based on several real data sets to demonstrate the fitting ability of the introduced distribution.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, a new three-parameter lifetime distribution is proposed by mixing modified Weibull and generalized gamma distributions.
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Temel Bulgular & Veri:The point estimation on the distribution parameters are discussed through several estimators.
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Sonuç & Katkı:The distribution modeling analyses are provided based on several real data sets to demonstrate the fitting ability of the introduced distribution.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Confidence interval · data analysis · lifetime distribution

Abstract

In this paper, a new three-parameter lifetime distribution is proposed by mixing modified Weibull and generalized gamma distributions. The point estimation on the distribution parameters are discussed through several estimators. The interval estimation is also studied with two methods based on asymptotic normality and likelihood ratio. A Monte Carlo simulation study is performed to evaluate the biases and mean square errors behaviors of point estimates for a different sample of size. A simulation study is also conducted to investigate the coverage probabilities of confidence intervals. The distribution modeling analyses are provided based on several real data sets to demonstrate the fitting ability of the introduced distribution.

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Bu Makaleye Atıf Yap

Kuş, C., Korkmaz, M. Ç., Kınacı, İ., Karakaya, K., Akdoğan, Y. (2022). Modified-Lindley distribution and its applications to the real data. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 1. https://doi.org/10.31801/cfsuasmas.744141

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Kaynakça (32)

  1. Alizadeh, M., MirMostafaee, S. M. T. K., Ghosh, I., A new extension of power Lindley distribution for analyzing bimodal data, Chilean Journal of Statistics, 8(1) (2017), 67–86.
  2. Almazah, M. M. A., Erbayram, T., Akdogan, Y., Al Sobhi, M. M., Afify, A. Z., A new extended geometric distribution: properties, regression model, and actuarial applications, Mathematics, 9(12) (2021), 1336. https://doi.org/10.3390/math9121336
  3. Altun, G., Alizadeh, M., Altun, E., Ozel, G., Odd Burr Lindley distribution with properties and applications, Hacettepe Journal of Mathematics and Statistics, 46(2) (2017), 255–276. https://doi.org/10.15672/HJMS.2017.410
  4. Asgharzadeh, A., Nadarajah, S., Sharafi, F., Weibull Lindley distribution, REVSTAT Statistical Journal, 16 (2018), 87–113.
  5. Bebbington, M., Lai, C. D., Zitikis, R., A flexible Weibull extension, Reliability Engineering and System Safety, 92(6) (2007), 719–726. https://doi.org/10.1016/j.ress.2006.03.004
  6. Bakouch, H. S., Al-Zahrani, B. M., Al-Shomrani, A. A., Marchi, V. A., Louzada, F., An extended Lindley distribution, Journal of the Korean Statistical Society, 41(1) (2012), 75–85. https://doi.org/10.1016/j.jkss.2011.06.002
  7. Bekker, A., Roux, J., Mostert, P., A generalization of the compound Rayleigh distribution: using a Bayesian methods on cancer survival times, Communications in Statistics - Theory and Methods, 29 (2000), 1419–1433. https://doi.org/10.1080/03610920008832554
  8. Carrasco, J. M., Ortega, E. M., Cordeiro, G. M., A generalized modified Weibull distribution for lifetime modeling, Computational Statistics & Data Analysis, 53(2) (2008), 450–462. http://dx.doi.org/10.1016/j.csda.2008.08.023
  9. Cheng, R. C. H., Amin, N. A. K., Maximum product of spacings estimation with application to the lognormal distribution, Mathematical Reports, (1979), 791.
  10. Fraser, D.A S., Probability and Statistics: Theory and Applications, North Scituate MA: Duxbury Press, 1976.
  11. Gomez-Deniz, E., Calderin-Ojeda, E., The discrete Lindley distribution: properties and applications, Journal of Statistical Computation and Simulation, 81(11) (2011), 1405-1416. https://doi.org/10.1080/00949655.2010.487825
  12. Ghitany, M.E., Al-Mutairi, D.K., Balakrishnan, N., Al-Enezi, L.J., Power Lindley distribution and associated inference, Computational Statistics and Data Analysis, 64 (2013), 20–33. https://doi.org/10.1016/j.csda.2013.02.026
  13. Karakaya, K., Tanıs, C. Estimating the parameters of Xgamma Weibull distribution, Adıyaman University Journal of Science, 10(2) (2020), 557–571. https://doi.org/10.37094/adyujsci.781069
  14. Karakaya, K., Tanıs, C. Different methods of estimation for the one parameter Akash distribution, Cumhuriyet Science Journal, 41(4) (2020), 944–950. https://doi.org/10.17776/csj.766011
  15. Korkmaz, M. C., Hamedani, G. G., An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications, Mathematica Slovaca, 70(4) (2020), 953–978. https://doi.org/10.1515/ms-2017-0406
  16. Kuş, C., Akdoğan, Y., Asgharzadeh, A., Kınacı, İ., Karakaya, K., Binomial-discrete Lindley distribution, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1) (2018), 401–411.
  17. Lai, C. D., Xie, M., Murthy, D. N. P., A modified Weibull distribution, IEEE Transactions on Reliability, 52(1) (2003), 33–37.
  18. Lindley, D.V., Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society Series B, 20 (1958), 102–107.
  19. Lucena, S. E., Silva, A. H. A., Cordeiro, G. M., The transmuted generalized gamma distribution: properties and application, Journal of Data Science, 13(1) (2015), 187–206.
  20. Merovci, F., Sharma, V. K., The beta-Lindley distribution: properties and applications, Journal of Applied Mathematics, Article ID 198951, (2014), 1–10. https://doi.org/10.1155/2014/198951
  21. MirMostafaee, S. M. T. K., Mahdizadeh, M., Nadarajah, S., The beta Lindley distribution, Journal of Data Science, 13(3) (2015), 603–625.
  22. Nadarajah, S., Bakouch, H. S., Tahmasbi, R., A generalized Lindley distribution, Sankhya B, 73(2) (2011), 331–359. http://doi.org/10.1007/s13571-011-0025-9
  23. Nichols, M.D., Padgett, W. J., A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22 (2006), 141–151. http://doi.org/10.1002/qre.691
  24. Ozel, G., Alizadeh, M., Cakmakyapan, S., Hamedani, G. G., Ortega, E. M., Cancho, V. G., The odd log-logistic Lindley Poisson model for lifetime data, Communications in Statistics-Simulation and Computation, 46(8) (2017), 6513–6537. https://doi.org/10.1080/03610918.2016.1206931
  25. Ramesh, C., Gupta, S.N.U.A., Kirmani, On order relations between reliability measures, Stochastic Models, 3(1) (1987), 149–156.
  26. Salman S. M., Prayoto, S., Total time on test plot analysis for mechanical components of the RSG-GAS reactor, Atom Indones, 25(2) (1999), 155–161.
  27. Shaked, M., Shanthikumar, J. G., Stochastic Orders, Springer Verlag, New York, 2007.
  28. Stacy, E. W., A generalization of the gamma distribution, The Annals of Mathematical Statistics, 33(3) (1962), 1187–1192.
  29. Tanış, C., On transmuted power function distribution: characterization, risk measures, and estimation, Journal of New Theory, 34 (2021), 72–81.
  30. Tanış, C., Karakaya, K., On estimating parameters of Lindley-geometric distribution, Eskisehir Technical University Journal of Science and Technology A-Applied Sciences and Engineering, 22(2) (2021), 160–167. https://doi.org/10.18038/estubtda.816836
  31. Warahena-Liyanage, G., Pararai, M., A generalized power Lindley distribution with applications, Asian Journal of Mathematics and Applications, (2014).
  32. Zakerzadeh, H., Dolati, A., Generalized Lindley distribution, Journal of Mathematical Extension, 3(2) (2009).