Research Article
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Year 2020, , 21 - 31, 15.10.2020
https://doi.org/10.36753/mathenot.752965

Abstract

References

  • Adamidis K., Loukas, S.: A lifetime distribution with decreasing failure rate. Stat Probab Lett. 39 (1), 35-42 (1998). https://doi.org/10.1016/S0167-7152(98)00012-1
  • Kus, C.: A new lifetime distribution. Comput Stat Data Anal. 51 (9), 4497–4509 (2007). https://doi.org/10.1016/j.csda.2006.07.017.
  • Tahmasbi, R., Rezaei, S.: A two-parameter lifetime distribution with decreasing failure rate. Comput Stat Data Anal. 52 (8), 3889–3901 (2008). https://doi.org/10.1016/j.csda.2007.12.002
  • Chahkandi, M., Ganjali, M.: On some lifetime distributions with decreasing failure rate. Comput Stat Data Anal. 53 (12), 4433–4440 (2009). https://doi.org/10.1016/j.csda.2009.06.016
  • Barreto-Souza, W., Bakouch, H.S.: A new lifetime model with decreasing failure rate. Statistics. 47 (2), 465–476 (2013) https://doi.org/10.1080/02331888.2011.595489
  • Lu, W., Chiang, J. Y.: On some life distributions with flexible failure rate. Quality Technology & Quantitative Management. 15 (3), 413-433 (2018). https://doi.org/10.1080/16843703.2016.1226596
  • Gui, W., Zhang, S., Lu, X.: The Lindley-Poisson distribution in lifetime analysis and its properties. Hacet J Math Stat. 43 (6), 1063–1077 (2014).
  • Yilmaz, M., Hameldarbandi, M., Kemaloglu, S.A.: Exponential-modified discrete Lindley distribution. SpringerPlus. 5 (1660), (2016b). https://doi.org/10.1186/s40064-016-3302-2
  • Bhaumik, D.K., Kapur, K., Gibbons, R.D.: Testing Parameters of a Gamma Distribution for Small Samples. Technometrics. 51, 326–334 (2009). https://doi.org/10.1198/tech.2009.07038
  • Maguire, B.A., Pearson, E.S., Wynn, A.H.A.: The time intervals between industrial accidents. Biometrika. 39 (1/2), 168–180 (1952). https://doi.org/10.2307/2332475
  • Yilmaz, M., Potas, N., Buyum, B.: A Classical Approach to Modeling of Coal Mine Data. In: Erçetin ¸S. (eds) Chaos, Complexity and Leadership 2014. Springer Proceedings in Complexity. Springer, Cham. Chapter 7, 65-72 (2016). https://doi.org/10.1007/978-3-319-18693-1_7
  • Mahdavi, A. and Kundu, D.: A New Method for Generating Distributions with an Application to Exponential Distribution. Communications in Statistics-Theory and Methods. 46 (13), 6543-6557 (2017). https://doi.org/10.1080/03610926.2015.1130839

Exponential-Discrete Lindley Distribution: Properties and Applications

Year 2020, , 21 - 31, 15.10.2020
https://doi.org/10.36753/mathenot.752965

Abstract

In this paper, we introduce a new compounding distribution named Exponential Discrete Lindley distribution which compounds the discrete Lindley distribution and exponential distribution. We obtain several
properties of the new distribution such as its probability density function, survival function, hazard rate
function, mean residual life function. Moments and expression for the Rényi entropy of the proposed
distribution are also given. Moreover, the maximum likelihood method using the EM algorithm is developed for
parameter estimation. Two real data sets are used to illustrate the usefulness of the proposed distribution

References

  • Adamidis K., Loukas, S.: A lifetime distribution with decreasing failure rate. Stat Probab Lett. 39 (1), 35-42 (1998). https://doi.org/10.1016/S0167-7152(98)00012-1
  • Kus, C.: A new lifetime distribution. Comput Stat Data Anal. 51 (9), 4497–4509 (2007). https://doi.org/10.1016/j.csda.2006.07.017.
  • Tahmasbi, R., Rezaei, S.: A two-parameter lifetime distribution with decreasing failure rate. Comput Stat Data Anal. 52 (8), 3889–3901 (2008). https://doi.org/10.1016/j.csda.2007.12.002
  • Chahkandi, M., Ganjali, M.: On some lifetime distributions with decreasing failure rate. Comput Stat Data Anal. 53 (12), 4433–4440 (2009). https://doi.org/10.1016/j.csda.2009.06.016
  • Barreto-Souza, W., Bakouch, H.S.: A new lifetime model with decreasing failure rate. Statistics. 47 (2), 465–476 (2013) https://doi.org/10.1080/02331888.2011.595489
  • Lu, W., Chiang, J. Y.: On some life distributions with flexible failure rate. Quality Technology & Quantitative Management. 15 (3), 413-433 (2018). https://doi.org/10.1080/16843703.2016.1226596
  • Gui, W., Zhang, S., Lu, X.: The Lindley-Poisson distribution in lifetime analysis and its properties. Hacet J Math Stat. 43 (6), 1063–1077 (2014).
  • Yilmaz, M., Hameldarbandi, M., Kemaloglu, S.A.: Exponential-modified discrete Lindley distribution. SpringerPlus. 5 (1660), (2016b). https://doi.org/10.1186/s40064-016-3302-2
  • Bhaumik, D.K., Kapur, K., Gibbons, R.D.: Testing Parameters of a Gamma Distribution for Small Samples. Technometrics. 51, 326–334 (2009). https://doi.org/10.1198/tech.2009.07038
  • Maguire, B.A., Pearson, E.S., Wynn, A.H.A.: The time intervals between industrial accidents. Biometrika. 39 (1/2), 168–180 (1952). https://doi.org/10.2307/2332475
  • Yilmaz, M., Potas, N., Buyum, B.: A Classical Approach to Modeling of Coal Mine Data. In: Erçetin ¸S. (eds) Chaos, Complexity and Leadership 2014. Springer Proceedings in Complexity. Springer, Cham. Chapter 7, 65-72 (2016). https://doi.org/10.1007/978-3-319-18693-1_7
  • Mahdavi, A. and Kundu, D.: A New Method for Generating Distributions with an Application to Exponential Distribution. Communications in Statistics-Theory and Methods. 46 (13), 6543-6557 (2017). https://doi.org/10.1080/03610926.2015.1130839
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sibel Açık Kemaloğlu 0000-0003-0449-6966

Mehmet Yılmaz 0000-0002-9762-6688

Publication Date October 15, 2020
Submission Date June 15, 2020
Acceptance Date August 2, 2020
Published in Issue Year 2020

Cite

APA Açık Kemaloğlu, S., & Yılmaz, M. (2020). Exponential-Discrete Lindley Distribution: Properties and Applications. Mathematical Sciences and Applications E-Notes, 8(2), 21-31. https://doi.org/10.36753/mathenot.752965
AMA Açık Kemaloğlu S, Yılmaz M. Exponential-Discrete Lindley Distribution: Properties and Applications. Math. Sci. Appl. E-Notes. October 2020;8(2):21-31. doi:10.36753/mathenot.752965
Chicago Açık Kemaloğlu, Sibel, and Mehmet Yılmaz. “Exponential-Discrete Lindley Distribution: Properties and Applications”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 21-31. https://doi.org/10.36753/mathenot.752965.
EndNote Açık Kemaloğlu S, Yılmaz M (October 1, 2020) Exponential-Discrete Lindley Distribution: Properties and Applications. Mathematical Sciences and Applications E-Notes 8 2 21–31.
IEEE S. Açık Kemaloğlu and M. Yılmaz, “Exponential-Discrete Lindley Distribution: Properties and Applications”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 21–31, 2020, doi: 10.36753/mathenot.752965.
ISNAD Açık Kemaloğlu, Sibel - Yılmaz, Mehmet. “Exponential-Discrete Lindley Distribution: Properties and Applications”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 21-31. https://doi.org/10.36753/mathenot.752965.
JAMA Açık Kemaloğlu S, Yılmaz M. Exponential-Discrete Lindley Distribution: Properties and Applications. Math. Sci. Appl. E-Notes. 2020;8:21–31.
MLA Açık Kemaloğlu, Sibel and Mehmet Yılmaz. “Exponential-Discrete Lindley Distribution: Properties and Applications”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 21-31, doi:10.36753/mathenot.752965.
Vancouver Açık Kemaloğlu S, Yılmaz M. Exponential-Discrete Lindley Distribution: Properties and Applications. Math. Sci. Appl. E-Notes. 2020;8(2):21-3.

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