Modified-Lindley distribution and its applications to the real data

Coşkun Kuş; Mustafa Çağatay Korkmaz; İsmail Kınacı; Kadir Karakaya; Yunus Akdoğan

doi:10.31801/cfsuasmas.744141

Research Article

Year 2022, Volume: 71 Issue: 1, 252 - 272, 30.03.2022

Coşkun Kuş Mustafa Çağatay Korkmaz İsmail Kınacı Kadir Karakaya Yunus Akdoğan

https://doi.org/10.31801/cfsuasmas.744141

Cited By: 6

Abstract

References

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.
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
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
Asgharzadeh, A., Nadarajah, S., Sharafi, F., Weibull Lindley distribution, REVSTAT Statistical Journal, 16 (2018), 87–113.
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
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
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
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
Cheng, R. C. H., Amin, N. A. K., Maximum product of spacings estimation with application to the lognormal distribution, Mathematical Reports, (1979), 791.
Fraser, D.A S., Probability and Statistics: Theory and Applications, North Scituate MA: Duxbury Press, 1976.
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
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
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
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
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
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.
Lai, C. D., Xie, M., Murthy, D. N. P., A modified Weibull distribution, IEEE Transactions on Reliability, 52(1) (2003), 33–37.
Lindley, D.V., Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society Series B, 20 (1958), 102–107.
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.
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
MirMostafaee, S. M. T. K., Mahdizadeh, M., Nadarajah, S., The beta Lindley distribution, Journal of Data Science, 13(3) (2015), 603–625.
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
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
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
Ramesh, C., Gupta, S.N.U.A., Kirmani, On order relations between reliability measures, Stochastic Models, 3(1) (1987), 149–156.
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.
Shaked, M., Shanthikumar, J. G., Stochastic Orders, Springer Verlag, New York, 2007.
Stacy, E. W., A generalization of the gamma distribution, The Annals of Mathematical Statistics, 33(3) (1962), 1187–1192.
Tanış, C., On transmuted power function distribution: characterization, risk measures, and estimation, Journal of New Theory, 34 (2021), 72–81.
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
Warahena-Liyanage, G., Pararai, M., A generalized power Lindley distribution with applications, Asian Journal of Mathematics and Applications, (2014).
Zakerzadeh, H., Dolati, A., Generalized Lindley distribution, Journal of Mathematical Extension, 3(2) (2009).

Modified-Lindley distribution and its applications to the real data

Year 2022, Volume: 71 Issue: 1, 252 - 272, 30.03.2022

Coşkun Kuş Mustafa Çağatay Korkmaz İsmail Kınacı Kadir Karakaya Yunus Akdoğan

https://doi.org/10.31801/cfsuasmas.744141

Cited By: 6

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.

Keywords

Confidence interval, data analysis, lifetime distribution, Lindley distribution, point estimates

References

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.
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
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
Asgharzadeh, A., Nadarajah, S., Sharafi, F., Weibull Lindley distribution, REVSTAT Statistical Journal, 16 (2018), 87–113.
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
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
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
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
Cheng, R. C. H., Amin, N. A. K., Maximum product of spacings estimation with application to the lognormal distribution, Mathematical Reports, (1979), 791.
Fraser, D.A S., Probability and Statistics: Theory and Applications, North Scituate MA: Duxbury Press, 1976.
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
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
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
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
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
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.
Lai, C. D., Xie, M., Murthy, D. N. P., A modified Weibull distribution, IEEE Transactions on Reliability, 52(1) (2003), 33–37.
Lindley, D.V., Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society Series B, 20 (1958), 102–107.
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.
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
MirMostafaee, S. M. T. K., Mahdizadeh, M., Nadarajah, S., The beta Lindley distribution, Journal of Data Science, 13(3) (2015), 603–625.
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
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
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
Ramesh, C., Gupta, S.N.U.A., Kirmani, On order relations between reliability measures, Stochastic Models, 3(1) (1987), 149–156.
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.
Shaked, M., Shanthikumar, J. G., Stochastic Orders, Springer Verlag, New York, 2007.
Stacy, E. W., A generalization of the gamma distribution, The Annals of Mathematical Statistics, 33(3) (1962), 1187–1192.
Tanış, C., On transmuted power function distribution: characterization, risk measures, and estimation, Journal of New Theory, 34 (2021), 72–81.
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
Warahena-Liyanage, G., Pararai, M., A generalized power Lindley distribution with applications, Asian Journal of Mathematics and Applications, (2014).
Zakerzadeh, H., Dolati, A., Generalized Lindley distribution, Journal of Mathematical Extension, 3(2) (2009).

There are 32 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Coşkun Kuş 0000-0002-7176-0176 Mustafa Çağatay Korkmaz 0000-0003-3302-0705 İsmail Kınacı 0000-0002-0992-4133 Kadir Karakaya 0000-0002-0781-3587 Yunus Akdoğan 0000-0003-3520-7493
Publication Date	March 30, 2022
Submission Date	May 28, 2020
Acceptance Date	August 18, 2021
Published in Issue	Year 2022 Volume: 71 Issue: 1

Cite

APA	Kuş, C., Korkmaz, M. Ç., Kınacı, İ., Karakaya, K., et al. (2022). Modified-Lindley distribution and its applications to the real data. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 252-272. https://doi.org/10.31801/cfsuasmas.744141
AMA	Kuş C, Korkmaz MÇ, Kınacı İ, Karakaya K, Akdoğan Y. Modified-Lindley distribution and its applications to the real data. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):252-272. doi:10.31801/cfsuasmas.744141
Chicago	Kuş, Coşkun, Mustafa Çağatay Korkmaz, İsmail Kınacı, Kadir Karakaya, and Yunus Akdoğan. “Modified-Lindley Distribution and Its Applications to the Real Data”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 252-72. https://doi.org/10.31801/cfsuasmas.744141.
EndNote	Kuş C, Korkmaz MÇ, Kınacı İ, Karakaya K, Akdoğan Y (March 1, 2022) Modified-Lindley distribution and its applications to the real data. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 252–272.
IEEE	C. Kuş, M. Ç. Korkmaz, İ. Kınacı, K. Karakaya, and Y. Akdoğan, “Modified-Lindley distribution and its applications to the real data”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 252–272, 2022, doi: 10.31801/cfsuasmas.744141.
ISNAD	Kuş, Coşkun et al. “Modified-Lindley Distribution and Its Applications to the Real Data”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 2022), 252-272. https://doi.org/10.31801/cfsuasmas.744141.
JAMA	Kuş C, Korkmaz MÇ, Kınacı İ, Karakaya K, Akdoğan Y. Modified-Lindley distribution and its applications to the real data. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:252–272.
MLA	Kuş, Coşkun et al. “Modified-Lindley Distribution and Its Applications to the Real Data”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 252-7, doi:10.31801/cfsuasmas.744141.
Vancouver	Kuş C, Korkmaz MÇ, Kınacı İ, Karakaya K, Akdoğan Y. Modified-Lindley distribution and its applications to the real data. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):252-7.