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Abstract
This article introduces a new three-parameter lifetime model with an increasing and bathtub failure rate functions as an extension of the Mustapha type II distribution (MuII). The model can be very useful in statistical studies, reliability, computer sciences and engineering. Various mathematical and statistical properties of the distribution are discussed, such as moments, mean deviations, Bonferroni and Lorenz curves, entropy, order statistic, and extreme value distributions. Moreover, we consider the bivariate extension of the new model. Statistical inferences by the maximum likelihood method are discussed and assess by simulation studies. Applications of the proposed model to two right-skewed data are presented for illustration. The new model provides a better fit than some other existing distribution as measured by some model selection criteria and goodness of fits statistics.
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References
-
Abdul-Moniem, I. B. (2015). Exponentiated nadarajah and haghighi exponential distribution. International j. of Mathematical Analysis and Applications (IJMAA), 2(5):68–73.
Abouammoh, A., Abdulghani, S., and Qamber, I. (1994). On partial orderings and testing of new better than renewal used classes. Reliability Engineering & System Safety, 43(1):37–41.
Arnold, Barry C., N. B. and Nagaraja, H. N. (1992). A first course in order statistics, volume 45. Siam.
Barreto-Souza, W. and Cribari-Neto, F. (2009). A generalization of the exponential-poisson distribution. Statistics & Probability Letters, 79(24):2493–2500.
Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49(2):155–161.
El-Gohary, A., Alshamrani, A., and Al-Otaibi, A. N. (2013). The generalized gompertz distribution. Applied Mathematical Modelling, 37(1):13–24.
Glaser, R. (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Associationl, 75:667–672.
Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: an alternative to gamma and weibull distributions. Biometrical journal, 43(1):117–130.
Hassan, A., Elshrpieny, E., and Mohammed, R. (2019). Odd generalized exponential power function distribution: Properties & applications. Gazi University Journal of Science, 32(1):351–370.
Jafari, A. A. and Tahmasebi, S. (2016). Gompertz-power series distributions. Communications in Statistics - Theory and Methods, 45(13):3761–3781.
Javanshiri, Z., Habibi Rad, A., and G Hamedani, H. (2013). Exp-uniform distribution: Properties and characterizations. Journal of Statistical Research of Iran JSRI, 10(1):85–106.
Kohansal, A. (2019). On estimation of reliability in a multicomponent stress-strength model for a kumaraswamy distribution based on progressively censored sample. Statistical Papers, 60(6):2185–2224.
Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of hydrology, 46(1-2):79–88.
Leadbetter, M. R., L. G. and Rootzen, H. (1987). Extremes and Related Properties of Random Sequences and Processes. Springer Verlag, New York.
Lemonte, A. J. (2013). A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Computational Statistics & Data Analysis, 62:149–170.
Lemonte, A. J., Barreto-Souza, W., and Cordeiro, G. M. (2013). The exponentiated kumaraswamy distribution and its log-transform. Braz. J. Probab. Stat., 27(1):31–53.
Mahmoud, M. A. and Alam, F. M. A. (2010). The generalized linear exponential distribution. Statistics & probability letters, 80(11-12):1005–1014.
Mudholkar, G. S. and Srivastava, D. (1993). Exponentiated weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42:299–302.
Muhammad, M. (2016a). A generalization of the burrxii-poisson distribution and its applications. Journal of Statistics Applications & Probability, 5(1):29–41.
Muhammad, M. (2016b). A new two parameter distribution with a finite support. Applied Mathematical Sciences. Accepted manuscript.
Muhammad, M. (2016c). Poisson-odd generalized exponential family of distributions: theory and applications. Hacettepe Journal of Mathematics and Statistics, 47(6):1652–1670.
Muhammad, M. (2017a). The complementary exponentiated burrxii poisson distribution : model , properties and application. Journal of Statistics Applications Probability, 6:33–48.
Muhammad, M. (2017b). Generalized half logistic poisson distributions. Communications for Statistical Applications and Methods, 24:353–365.
Muhammad, M. (2017c). A new lifetime model with a bounded support. Asian Research Journal of Mathematics,7:1–11.
Muhammad, M. and Yahaya, M. A. (2017). The half logistic-poisson distribution. Asian Journal of Mathematics and Applications, 2017:1–15.
Sarhan, A. M., Abd, E.-B. A., and Alasbahi, I. A. (2013). Exponentiated generalized linear exponential distribution. Applied Mathematical Modelling, 37(5):2838–2849.
Tahir, M. H. and Cordeiro, G. M. (2016). Compounding of distributions: a survey and new generalized classes. Journal of Statistical Distributions and Applications, 3(1):13.
Topp, C. W. and Leone, F. C. (1955). A family of j-shaped frequency functions. Journal of the American Statistical Association, 50(269):209–219.
Torabi, H. and Montazeri, N. H. (2014). The logistic-uniform distribution and its applications. Communications in Statistics-Simulation and Computation, 43(10):2551–2569.
Tu, J. and Gui,W. (2020). Bayesian inference for the kumaraswamy distribution under generalized progressive hybrid censoring. Entropy, 22(9):1032.
Warahena-Liyanage, G. and Pararai, M. (2014). A generalized power lindley distribution with applications. Asian Journal of Mathematics and Applications, 2014.