Transmuted Logistic-Exponential Distribution for Modelling Lifetime Data
Keywords:Failure rate, skewed data, quadratic rank and transmutation map
Logistic-exponential (LE) distribution is one of the rare distributions in existence for modeling lifetime data due to its unique features. It is the only two-parameter distribution with quintuplet characteristics of hazard failure rates. However, its limitation is inability to model extremely skewed real life situation phenomena appropriately. This study proposed, developed and studied a new transmuted logistic-exponential distribution with three parameters with the aim of increasing the shape flexibility of LE distribution that will be more applicable to skewed lifetime data in various fields. We adopt the cumulative distribution function of LE and the quadratic rank transmutation map (QRTM) function in its development. Its quantile, survival, hazard functions, order statistics, skewness and kurtosis were derived. Its hazard function was found to have increasing, decreasing and constant failure rates while the survival function has a decreasing shape. Again, the estimates of the parameters were obtained using maximum likelihood estimation technique. Its efficiency was examined using real life dataset. The maximum likelihood estimates obtained were compared with the existing similar distributions using Akaike information criteria (AIC) and log-likelihood. The result showed that the newly transmuted LE distribution outperformed other models fitted to the dataset. The fitness of the distributions was also examined using two goodness of fit test. Both Kolmogorov-Smirnov and Anderson-Darling tests statistics confirmed that NTLE has a good fit. Hence, the new transmuted logistic-exponential (NTLE) distribution is more appropriate in modeling skewed lifetime datasets. In future research, we intend to study some other properties of this newly transmuted distribution and compare different estimation procedures for its parameters.
Ali S, Dey S, Tahir MH, Mansoor M. Two-parameter logistic-exponential distribution: some new properties and estimation methods. Am J Math Manag Sci. 2020; 39(3): 270-298.
Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. Metron. 2013; 71(1): 63-79.
Everitt B. The Cambridge dictionary of statistics, Cambridge: Cambridge University Press. 2006.
Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc. 1825; 115: 513-585.
Gupta RC, Gupta PL, Gupta RD. Modelling failure time data by Lehman alternatives. Commun Stat Theory Methods. 1998; 27(4): 887-904.
Hasting JC, Mosteller F, Tukey JW, Windsor C. Low moments for small samples: a comparative study of order statistics. Ann Stat. 1947; 18: 413-426.
Johnson NL. Systems of frequency curves generated by methods of translation. Biometrika. 1949; 36: 149-176.
Kenney J, Keeping E. Mathematics of statistics, Volume 2, Van Nostrand: Princeton; 1962.
Khan MS, King R, Hudson IL. Transmuted Weibull distribution: properties and estimation. Commun Stat Theory Methods. 2016; 46(11): 5394-5418.
Lan Y, Leemis, LM. The logistic-exponential survival distribution. Nav Res Logist. 2008; 55(3): 252-264.
Lee ET, Wang JW. Statistical methods for survival data analysis. New York: John Wiley & Sons; 2003.
Mansoor M, Tahir MH, Cordeiro GM, Provost SB, Alzaatreh A. The Marshall-Olkin logistic-exponential distribution. Commun Stat Theory Methods. 2018; 48(2): 220-234.
Merovci F. Transmuted exponentiated exponential distribution. Math Sci Appl E-Notes. 2013; 1(2), 112-122.
Moors JJA. A quantile alternative for kurtosis. J R Stat Soc Ser D. 1988; 37(1), 25-32.
Owoloko EA, Oguntunde PE, Adejumo AO. Performance rating of the transmuted exponential distribution: an analytical approach. SpringerPlus. 2015; 4(1):1-15.
Pearson K. Contributions to the mathematical theory of evolution. Philos Trans R Soc. 1894; 185: 71-110.
Samuel AF. On the performance of transmuted logistic distribution: statistical properties and application. BirEx. 2019; 1(3): 26-34.
Shaw WT, Buckley IR. The alchemy of probability distributions: beyond Gram-Charlier and Cornish-Fisher expansions, and skew-normal or kurtotic-normal distributions. Proceedings of the first IMA computational Finance Conference; 2007 Feb 18; London. Available from: https://library.wolfram.com/infocenter/Articles/6670/alchemy.pdf
Tabassum NS, Zawar H, Muhammad A. Transmuted Burr Type X model with applications to life time data. In: Ali I, Cárdenas-Barrón LE, Ahmed A, Shaikh AA, editors. Optimal Decision Making in Operation, Research and Statistics: Methodologies and Application. Florida: Taylor & Francis Group; 2021. p. 43-58.
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