A Note on the Transmuted Generalized Inverted Exponential Distribution with Application to Reliability Data

  • Idika E. Okorie
  • Anthony C. Akpanta
Keywords: Reliability, unimodal, bathtub, maximum likelihood estimation


Based on the transmuted generalized inverted exponential (TGIE) distribution (Elbatal 2013), Khan (2018) revisited the TGIE distribution with an illustrative application to a reliability data-set. Here, we revisit the data application and discuss the inadequacy of the TGIE distribution to the applied data-set.


Download data is not yet available.


Aarset MV. How to identify a bathtub hazard rate. IEEE Transactions on Reliability. 1987; 36: 106-108.

Abouammoh AM, Alshingiti AM. Reliability estimation of generalized inverted exponential distribution. J Stat Comput Simulat. 2009; 79: 1301-1315.

Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr. 1974; 19: 716-23.

Bursa N, Ozel G. The exponentiated Kumaraswamy-power function distribution. Hacettepe J Math Stat. 2017; 46: 277-292.

Elbatal I. Transmuted generalized inverted exponential distribution. Econ Qual Contr. 2013; 28:125-133.

Gupta RD, Kundu D. Generalized exponential distribution: different method of estimations. J Stat ComputSimulat. 2001; 69: 315-337.

Hurvich CM, Tsai CL. Regression and time series model selection in small samples. Biometrika. 1989; 76: 297-307.

Javed M, Nawaz T, Irfan M. The Marshall-Olkin kappa distribution: properties and applications. J King Saud University-Science. 2018: 1-8

Khan MS. Transmuted generalized inverted exponential distribution with application to reliability data. Thail Stat. 2018; 16:14-25.

Kolmogorov A. Sulla determinazione empirica di una lgge di distribuzione. Inst Ital Attuari Giorn 1933; 4: 83-91.

Korkmaz MÇ, Altun E, Yousof HM, Afify AZ, Nadarajah S. The Burr X Pareto Distribution: Properties, Applications and VaR Estimation. J Risk Financ Manag. 2017; 11: 1-16.

Nassar M, Afify AZ, Dey S, Kumar D. A new extension of weibull distribution: Properties and different methods of estimation. J Comput Appl Math. 2017; 336: 439-457.

Oguntunde P, Adejumo O. The transmuted inverse exponential distribution. Int J Adv Stat Probab. 2014; 3: 1-7.

Okorie IE, Akpanta AC, Ohakwe J, Chikezie DC. The modified power function distribution. Cogent Mathematics. 2017a; 4(1), DOI: 10.1080/23311835.2017.1319592.

Okorie IE, Akpanta AC, Ohakwe J, Chikezie DC. The extended Erlang-truncated exponential distribution: properties and application to rainfall data. Heliyon. 2017b; 3: DOI:10.1016/ j.heliyon.2017.e00296

Scheffé H. Statistical inference in the non-parametric case. Ann Math Stat. 1943; 14: 305-332.

Schwarz G. Estimating the dimension of a model. Ann Stat. 1978; 6: 461-464.

Shaw WT, Buckley IR. The alchemy of probability distributions: beyond Gram-Charlier&Cornish-Fisher expansions, and skew-normal or kurtotic-normal distributions. Proceeding of IMA Conference on Computational Finance; 2007 March 23;
De Morgan House, London.

Smirnoff N. Sur les écarts de la courbe de distribution empirique. Matematicheskii Sbornik. 1939; 48: 3-26.

Tahir M, Alizadeh M, Mansoor M, Cordeiro GM, Zubair M. The Weibull-power function distribution with applications. Hacet J Math Stat. 2014; 45: 245-265.

Wolfowitz J. Non-parametric statistical inference. Proceedings of the Berkeley Symposium on mathematical statistics and probability; 1949; Berkeley, CA: University of California Press; 1948; 93-113.

Zakerzadeh H, Mahmoudi E. A new two parameter lifetime distribution: model and properties. arXiv:1204.4248. 2012.