The Cubic Rank Transmuted Inverse Exponential Distribution

PDF

Published: 2023-06-06

DOI: 10.56557/ajomcor/2023/v30i28262

Page: 17-25


N. P. Akpan *

Department of Mathematics and Statistics, University of Port Harcourt, Nigeria.

O. R. Uwaeme

Department of Mathematics and Statistics, University of Port Harcourt, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

This paper uses the recently proposed cubic rank transmutation technique to develop and propose a new distribution in the transmutation family called the Cubic Rank Transmuted Inverse Exponential distribution (CRTIE). Important mathematical properties of the new distribution including Quantile function, and Reliability analysis were derived. The estimates of the parameters of the new distribution were also derived.

Keywords: Inverse exponential distribution, cubic rank transmutation, Quantile function, hazard rate function, survival function, reliability analysis


How to Cite

Akpan , N. P., & Uwaeme , O. R. (2023). The Cubic Rank Transmuted Inverse Exponential Distribution. Asian Journal of Mathematics and Computer Research, 30(2), 17–25. https://doi.org/10.56557/ajomcor/2023/v30i28262

Downloads

Download data is not yet available.

References

Rahman MM, Al-Zahrani B, Shahbaz MQ. New general transmuted family of distributions with applications. Pakistan Journal of Statistics and Operation Research. 2018;807-829.

Shaw WT, Buckley IR. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv. 2009;0901.0434.

Aryal GR, Tsokos CP. Transmuted Weibull distribution: A generalization of theWeibull probability distribution. European Journal of pure and applied mathematics. 2011;4(2):89-102.

Merovci F. Transmuted exponentiated exponential distribution. Mathematical Sciences and Applications E-Notes. 2013;1(2):112-122.

Ahmad A, Ahmad SP, Ahmed A. Transmuted inverse rayleigh distribution: A generalization of the inverse Rayleigh distribution. Mathematical Theory and Modeling. 2014;4(7):90-98.

Afify AZ, Hamedani G, Ghosh I, Mead ME. The transmuted Marshall-Olkin Fréchet distribution: properties and applications. International Journal of Statistics and Probability. 2014;4(6):132–148.

Khan MS, King R, Hudson IL. Transmuted generalized exponential distribution: A generalization of the exponential distribution with applications to survival data. Communications in Statistics-Simulation and Computation. 2017;46(6):4377-4398.

Abdullahi UK Ieren TG. On the inferences and applications of transmuted exponential Lomax distribution. International Journal of Advanced Statistics and Probability. 2018;6(1):30-36.

Samuel AF. On the performance of transmuted logistic distribution: Statistical properties and application. Budapest International Research in Exact Sciences (BirEx) Journal. 2019;1(3):26-34.

Badr MM, Elbatal I, Jamal F, Chesneau C, Elgarhy M. The transmuted odd Fréchet-G family of distributions: Theory and applications. Mathematics. 2020;8(6):958.

Granzotto DCT, Louzada F, Balakrishnan N. Cubic rank transmuted distributions: inferential issues and applications. Journal of statistical Computation and Simulation. 2017;87(14):2760-2778.

AL-Kadim KA, Mohammed MH. The cubic transmuted Weibull distribution. Journal of University of Babylon. 2017;3:862-876.

Rahman MM, Al-Zahrani B, Shahbaz SH, Shahbaz MQ. Transmuted probability distributions: A review. Pakistan Journal of Statistics and Operation Research. 2020;83-94.

Bhatti FA, Hamedani GG, Sheng W, Ahmad M. Cubic rank transmuted modified burr III pareto distribution: Development, properties, characterizations and applications. International Journal of Statistics and Probability. 2019;8:94–112.

Ansari Sİ, Samuh M, Bazyari A. Cubic transmuted power function distribution. Gazi University Journal of Science. 2019;32(4):1322-1337.

Rahman MM, Al-Zahrani B, Shahbaz SH, Shahbaz MQ. Cubic transmuted uniform distribution: An alternative to beta and Kumaraswamy distributions. European Journal of Pure and Applied Mathematics. 2019;12(3):1106-1121.

Adeyinka FS. On Modelling of infant mortality rate in nigeria with exponentiated cubic transmuted exponential distribution. International Journal on Data Science and Technology. 2020;6(1):16-22.

Akter S, Khan MAI, Rana MS, Rahman MM. Cubic transmuted burr-xii distribution with properties and applications. Journal of Statistics Applications & Probability Letters. 2021;8(1):23-32.

Keller AZ, Kamath AR. Reliability analysis of cnc machine tools, Reliability Engineering. 1982;3:449-473.

Lin CT, Duran BS, Lewis TO. Inverted gamma as a life distribution. Microelectronics Reliability. 1989;29(4):619-626.

Abouammoh AM, Alshingiti AM. Reliability estimation of generalized inverted exponential distribution. Journal of Statistical Computation and Simulation. 2009;79(11):1301-1315.

Oguntunde PE, Adejumo AO, Owoloko EA. Exponential inverse exponential (EIE) distribution with applications to lifetime data. Asian Journal of Scientific Research. 2017;10(3):169-177.

Oguntunde PE, Adejumo A, Owoloko EA. Application of kumaraswamy inverse exponential distribution to real lifetime data. International Journal of Applied Mathematics and Statistics. 2017;56(5):34-47.

Oguntunde PE, Adejumo A, Owoloko EA. On the exponentiated generalized inverse exponential distribution.-Lecture Notes on engineering and computer science. Proceeding of the World Congress on Engineering (pp. 80-83). London, UK; 2017.

Ieren TG, Abdullahi J. Properties and applications of a two-parameter inverse exponential distribution with a decreasing failure rate. Pakistan Journal of Statistics. 2020;36(3):183-206.

Hyndman RJ, Fan Y. Sample quantiles in statistical packages. The American Statistician. 1996;50(4): 361-365.