Abstract
This paper provides a new three-parameter lifetime distribution with increasing and decreasing hazard function. The various statistical properties of the proposed distribution are also discussed. The maximum likelihood method is used for estimating the unknown parameters, and its performance is assessed using Monte-Carlo simulation. Finally, three real data sets are applied to illustrate the application of the proposed distribution.
Similar content being viewed by others
References
Aarest, M.V.: How to identify a bathtub hazard rate. IEEE Trans. Reliab. 36(1), 106–108 (1987)
Adamidis, K., Dimitrakopoulou, T., Loukas, S.: On an extension of the exponential-geometric distribution. Stat. Probability Latters 73(3), 259–269 (2005)
Adamidis, K., Loukas, S.: A lifetime distribution with decreasing failure rate. Stat. Probability Latters 39, 35–42 (1998)
Ahmad, Z., Elgarhy, M., Abbas, N.: A new extended alpha power transformed family of distributions: properties and applications. J. Stat. Model.: Theory Appl. 1(2), 13–28 (2018)
Baily, W.N.: Generalized Hypergeometric Series. University Press, Cambridge (1935)
Bjerkedal, T.: Acquisition of resistance in guinea pies infected with different doses of virulent tubercle bacilli. Am. J. Hyg. 72(1), 130–148 (1960)
Bordbar, F., Nematollahi, A.R.: The modified exponential-geometric distribution. Commun. Stat.-Theory Methods 45(1), 173–181 (2016)
Brunk, H.D., Barlow, R.E., Bartholomew, D.J., Bremner, J.M.: Stat. Inference under Order Restrict. Wiley, New York (1972)
Cordeiro, G.M., Silva, G.O., Ortega, E.M.: An extended-G geometric family. J. Stat. Distrib. Appl. 3(1), 1–16 (2016)
Cox, D.R.: Renew. Theory. Methuen, London (1962)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). J. Royal Stat. Soc.: Series B 39, 1–38 (1977)
Deshpande, JV: and Purohit. Statistical Models and Methods, World Scientific Publishing Company, S. G., Lifetime Data (2006)
Dahiya, R.C., Gurland, J.: Goodness of fit tests for the gamma and exponential distributions. Technometrics 14(3), 791–801 (1972)
Gleser, L.J.: The gamma distribution as a mixture of exponential distributions. Am. Stat. 43(2), 115–117 (1989)
Gupta, R.D., Kundu, D.: Generalized exponential distribution. Australian New Zealand J. Stat. 41, 173–188 (1999)
Gupta, R.D., Kundu, D.: Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom. J.: J. Math. Methods Biosci. 43(1), 117–130 (2001)
Gupta, R.D., Kundu, D.: Generalized exponential distribution: different method of estimations. J. Stat. Comput. Simul. 69(4), 315–337 (2001)
Gupta, R.D., Kundu, D.: Generalized exponential distribution: Existing results and some recent developments. J. Stat. Plan. Inference 137(11), 3537–3547 (2007)
Jodrá, P.: On a connection between the polylogarithm function and the Bass diffusion model. Proc. Royal Soc. A: Math., Phys. Eng. Sci. 464(2099), 3081–3088 (2008)
Kus, C.: A new lifetime distribution. Comput. Stat. Data Anal. 51(9), 4497–4509 (2007)
Lawless, J.F.: Statistical models and methods for lifetime data. Wiley, New York (2011)
Lewin, L.: Polylogarithms and associated functions. Elsevier, New York (1981)
Louzada, F., Marchi, V., Carpenter, J.: The complementary exponentiated exponential geometric lifetime distribution. J. Probability Stat. 2013, 1–12 (2013)
Louzada, F., Ramos, P.L., Perdon, G.S.: Different estimation procedures for the parameters of the extended exponential geometric distribution for medical data. Comput. Math. Methods Med. 2016, 1–12 (2016)
Maguire, B.A., Pearson, E.S., Wynn, A.H.A.: The time intervals between industrial accidents. Biometrika 39, 168–180 (1952)
Marshall, A.W., Olkin, I.: A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84(3), 641–652 (1997)
Mudholkar, G.S., Srivastava, D.K.: Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans. Reliab. 42(2), 299–302 (1993)
Nadarajah, S., Kotz, S.: The exponentiated type distributions. Acta Appl. Math. 9(2), 97–111 (2006)
Preda, V., Panaitescu, E., Ciumara, R.: The modified exponential-Poisson distribution. Proc. Rom. Academy 12(1), 22–29 (2011)
Proschan, F.: Theoretical explanation of observed decreasing failure rate. Technometrics 5(3), 375–383 (1963)
Prudnikov, A.P., Brychkov, Yu.A., Marichev, O.I.: Integrals and series. More special functions, vol. 3. Gordon and Breach, New York (1990)
Rasekhi, M., Alizadeh, M., Altun, E., Hamedani, G.G., Afify, A.Z., Ahmad, M.: The modified exponential distribution with applications. Pak. J. Stat. 33(5), 383–398 (2017)
Rényi, A., On measures of entropy and information, In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, The Regents of the University of California (1961)
Shannon, C.E.: Prediction and entropy of printed English. Bell Labs Tech. J. 30(1), 50–64 (1951)
Acknowledgements
The authors are thankful the associate editor and two anonymous referees for their useful comments, which led to the improved version of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zanboori, A., Zare, K. & Khodadadi, Z. A new modified exponential-geometric distribution: properties and applications. Math Sci 15, 413–424 (2021). https://doi.org/10.1007/s40096-021-00391-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40096-021-00391-8
Keywords
- Exponential distribution
- Hazard function
- Lifetime
- Monte-Carlo simulation
- New modified exponential-geometric distribution