On the Properties and Applications of a Transmuted Lindley-Exponential Distribution

Main Article Content

Adamu Abubakar Umar
Innocent Boyle Eraikhuemen
Peter Oluwaseun Koleoso
Jerry Joel
Terna Godfrey Ieren

Abstract

The Quadratic rank transmutation map proposed for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter has been used by several authors and is proven to be useful. This article uses this method to add flexibility to the Lindley-Exponential distribution which results to a new continuous distribution called “transmuted Lindley-Exponential distribution”. This paper presents the definition, validation, properties, application and estimation of unknown parameters of the transmuted Lindley-Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to a real life dataset on the survival times (in days) of 72 guinea pigs and the result gives good evidence that the transmuted Lindley-Exponential distribution is better than the Lindley-Exponential distribution, Exponential distribution and Lindley distribution based on the dataset used.

Keywords:
Quadratic rank transmutation map, Transmuted Lindley-Exponential distribution, definition, properties, maximum likelihood estimation, applications.

Article Details

How to Cite
Umar, A. A., Eraikhuemen, I. B., Koleoso, P. O., Joel, J., & Ieren, T. G. (2019). On the Properties and Applications of a Transmuted Lindley-Exponential Distribution. Asian Journal of Probability and Statistics, 5(3), 1-13. https://doi.org/10.9734/ajpas/2019/v5i330139
Section
Original Research Article

References

Oguntunde PE, Adejumo AO, Okagbue HI, Rastogi MK. Statistical properties and applications of a new lindley exponential distribution. Gazi University Journal of Science, GU J Sci. 2016;29(4): 831-838.

Ieren TG, Kuhe AD. On the properties and applications of Lomax-exponential distribution. Asian Journal of Probability and Statistics. 2018;1(4):1-13.

Abdullahi J, Abdullahi UK, Ieren TG, Kuhe DA, Umar AA. On the properties and applications of transmuted odd generalized exponential- exponential distribution. Asian Journal of Probability and Statistics. 2018;1(4):1-14.

Owoloko EA, Oguntunde PE, Adejumo AO. Performance rating of the transmuted exponential distribution: an analytical approach. Spring. 2015;4:818-829.

Oguntunde PE, Adejumo AO. The transmuted inverse exponential distribution. Inter. J. Adv. Stat. Prob. 2015;3(1):1–7.

Maiti SS, Pramanik S. Odds generalized exponential-exponential distribution. J. of Data Sci. 2015; 13:733-754.

Yahaya A, Ieren TG. On transmuted Weibull-exponential distribution: Its properties and applications. Nigerian J. of Sci. Res. 2017;16(3):289-297.

Oguntunde PE, Balogun OS, Okagbue HI, Bishop SA. The Weibull-exponential distribution: Its properties and applications. J. Appl. Sci. 2015;15(11):1305-1311.

Shaw WT, Buckley IR. The alchemy of probability distributions: Beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report; 2007.

R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2019.
Available:https://www.R-project.org/

Bjerkedal T. Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. Am. J. Hyg. 1960;72:130-148.

Merovci F. The transmuted rayleigh distribution. Austr. J. Stat. 2013;22(1):21–30.

Merovci F, Puka I. Transmuted pareto distribution. Prob. Stat. Forum. 2014;7:1–11.

Abdullahi UK, Ieren TG. On the inferences and applications of transmuted exponential Lomax distribution. Int. J. of Adv. Prob. Stat. 2018;6(1):30-36.