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Abstract

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

Keywords

Erlang-truncated Exponential distribution McDonald distribution moments Moment generating function Maximum Likelihood Estimation.

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Author Biography

Ibrahim Elbatal

Professor of Mathematical Statistics Department
How to Cite
Elbatal, I., & Aldukeel, A. (2021). On Erlang-Truncated Exponential Distribution: Theory and Application. Pakistan Journal of Statistics and Operation Research, 17(1), 155-168. https://doi.org/10.18187/pjsor.v17i1.2963
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References

  1. Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108.
  2. Bjerkedal, T. (1960). Acquisition of resistance in Guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Hygiene, 72, 130-148.
  3. Alizadeh, M., Jamal, F., Yousof, H. M., Khanahmadi, M. and Hamedani, G. G. (2020). Flexible Weibull generated family of distributions: characterizations, mathematical properties and applications. University Politehnica of Bucharest Scientific Bulletin-Series A- Applied Mathematics and Physics, 82(1), 145-150.â€
  4. Alizadeh, M., Lak, F., Rasekhi, M., Ramires, T. G., Yousof, H. M. and Altun, E. (2018). The odd log-logistic Topp-Leone G family of distributions: heteroscedastic regression models and applications. Computational Statistics, 33(3), 1217-1244.â€
  5. Cordeiro, G. M. and Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation. 81(7), 883-898.
  6. Cordeiro, G. M. Cintra, R. J., Rêgo, L. C. and Ortega, E. M. M. (2012). The McDonald normal distribution. Pakistan Journal of Statistics and Operation Research, 8(3), 301-329.
  7. El-Alosey,A. R (2007). Random sum of new type of mixture of distribution, International Journal of Statistics and Systems, 2, 49-57.
  8. Elbiely, M. M. and Yousof, H. M. (2019). A new flexible Weibull Burr XII distribution. Journal of Statistics and Applications, 2(1), 59-77.â€
  9. Eugene, N., Lee, C., Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods 31(4), 497-512.
  10. Gradshteyn, I. S. and Ryzhik, I. M. (2000). Table of Integrals, Series, and Products (sixth edition). San Diego: Academic Press.
  11. Gross, J. and Clark, V. A. (1975). Survival Distributions: Reliability Applications in the Biometrical Sciences, John Wiley, New York, USA
  12. Guess, F. and Proschan, F. (1988). Mean residual life: theory and applications. In Handbook of Statistics (P. R. Krishnaiah and C. R. Rao, eds.) 7 215-224. North-Holland, New York
  13. Gupta, R. C. (1981) On the mean residual life function in survival studies, Distributions in Scientific Work 5, D-Reidel Publishing Co. Boston, 327-334.
  14. Hamedani, G. G., Altun, E., Korkmaz, M. Ç., Yousof, H. M., & Butt, N. S. (2018). A new extended G family of continuous distributions with mathematical properties, characterizations and regression modeling. Pakistan Journal of Statistics and Operation Research, 737-758.â€
  15. Ibrahim, M. and Yousof, H. (2020). Transmuted Topp-Leone Weibull lifetime distribution: Statistical properties and different method of estimation. Pakistan Journal of Statistics and Operation Research, 501-515.
  16. Ibrahim, M., Altun, E. and Yousof, H. M. (2020). A new distribution for modeling lifetime data with different methods of estimation and censored regression modeling. Statistics, Optimization & Information Computing, 8(2), 610-630.â€
  17. Karamikabir, H., Afshari, M., Yousof, H. M., Alizadeh, M., & Hamedani, G. (2020). The Weibull Topp-Leone Generated Family of Distributions: Statistical Properties and Applications. Journal of The Iranian Statistical Society, 19(1), 121-161.â€
  18. Korkmaz, M. Ç., Alizadeh, M., Yousof, H. M. and Butt, N. S. (2018). The generalized odd Weibull generated family of distributions: statistical properties and applications. Pakistan Journal of Statistics and Operation Research, 541-556.â€
  19. Korkmaz, M. Ç., Altun, E., Yousof, H. M. and Hamedani, G. G. (2019a). The odd power Lindley generator of probability distributions: properties, characterizations and regression modeling. International Journal of Statistics and Probability.†8(2), 70-89.
  20. Korkmaz, M. Ç., Altun, E., Yousof, H. M. and Hamedani, G. G. (2020). The Hjorth's IDB Generator of Distributions: Properties, Characterizations, Regression Modeling and Applications. Journal of Statistical Theory and Applications, 19(1), 59-74.â€
  21. Korkmaz, M. Ç., Cordeiro, G. M., Yousof, H. M., Pescim, R. R., Afify, A. Z. and Nadarajah, S. (2019b). The Weibull Marshall-Olkin family: Regression model and application to censored data. Communications in Statistics-Theory and Methods, 48(16), 4171-4194.â€
  22. Korkmaz, M. C., Yousof, H. M., Alizadeh, M. and Hamedani, G. G. (2019c). The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1506-1527.â€
  23. Kundu, D., Nanda, A.K., 2010. Some reliability properties of the inactivity time. Communications in Statistics-Theory and Methods 39, 899-911.
  24. Lai, C. D and Xie, M (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.
  25. Marciano, F. W. P., Nascimento, A. D. C., Santos-Neto, M., and Cordeiro, G. M. (2012). The Mc- Γ distribution and its statistical properties: An application to reliability data. International Journal of Statistics and Probability, 1(1), 53-71.
  26. Mi, J (1996). Limiting Behavior of Mixtures of Discrete Lifetime Distributions. Naval Researc Logistics, 43, 365-380.
  27. Nasiru, S., Luguterah, A. and Iddrisu, M.M. (2016). Generalized Erlang-truncated exponential distribution, Adv. Appl. Stat. 48(4), 273-301.
  28. Okorie, I. E., Akpanta A. C. and Ohakwe, J. (2017). Marshall-Olkin generalized Erlang-truncated exponential distribution: Properties and applications. Cogent Mathematics, 4, 1-19.
  29. Okorie, I. E., Akpanta A. C. and Ohakwe, J. (2016). Transmuted Erlang-truncated exponential distribution, Econ. Qual. Control 31(2), 71-84.
  30. Oliveira, J., Santos, J., Xavier, C., Trindade, D., and Cordeiro, G. M. (2013). The McDonald half-logistic distribution: Theory and practice. Communications in Statistics-Theory and Methods, 10.1080/03610926.2013.873131.
  31. Oluyede, B. O. and Rajasooriya, S. (2013). The Mc-Dagum distribution and its statistical properties with applications. Asian Journal of Mathematics and Applications, 2013, 1-16.
  32. Parzen, E. (1962). On Estimation of a Probability Density Function and Mode. The Annals of Mathematical Statistics. 33 (3), 1065-1076.
  33. Roozegar, R., Tahmasebi, S. and Jafari, A. A. (2017). The McDonald Gompertz distribution: properties and applications, 47(5), 3341-3355.
  34. Rosenblatt, M. (1956). Remarks on Some Nonparametric Estimates of a Density Function. The Annals of Mathematical Statistics. 27 (3), 832-837. doi:10.1214/aoms/1177728190
  35. Yousof, H. M., Altun, E., Rasekhi, M., Alizadeh, M., Hamedani, G. G. and Ali, M. M. (2019). A new lifetime model with regression models, characterizations and applications. Communications in Statistics-Simulation and Computation, 48(1), 264-286.â€
  36. Yousof, H. M., Majumder, M., Jahanshahi, S. M. A., Masoom Ali, M. and Hamedani, G. G. (2018a). A new Weibull class of distributions: theory, characterizations and applications. Journal of Statistical Research of Iran JSRI, 15(1), 45-82.â€
  37. Yousof, H., Mansoor, M., Alizadeh, M., Afify, A. and Ghosh, I. (2020). The Weibull-G Poisson family for analyzing lifetime data. Pakistan Journal of Statistics and Operation Research, 131-148.â€
  38. Yousof, H. M., Rasekhi, M., Alizadeh, M. and Hamedani, G. G. (2018b). The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications and characterizations. Journal of Nonlinear Sciences and Applications, 13(1), 34-52
  39. Yousof, H. M., Rasekhi, M., Altun, E. and Alizadeh, M. (2018c). The extended odd Frechet family of distributions: properties, applications and regression modeling. International Journal of Applied Mathematics and Statistics, 30(1), 1-30.â€