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Article Content:-
Abstract
In this article, a three-parameter continuous distribution is introduced called Logistic inverse Lomax distribution. We have discussed some mathematical and statistical properties of the distribution such as the probability density function, cumulative distribution function and hazard rate function, survival function, quantile function, the skewness, and kurtosis measures. The model parameters of the proposed distribution are estimated using three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. The goodness of fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real data set.
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References
Birnbaum, Z.W., & Saunders, S.C. (1969). Estimation for a family of life distributions with applications to fatigue, Journal of Applied Probability, 6, 328 -347.
Chaudhary, A. K. & Kumar, V. (2020). Half logistic exponential extension distribution with Properties and Applications. International Journal of Recent Technology and Engineering (IJRTE), 8(3), 506-512.
Chaudhary, A. K. & Kumar, V. (2020). Lindley half Cauchy distribution: Properties and Applications. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(9), 1233-1242.
Gupta, R. D., & Kundu, D. (2007). Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference, 137(11), 3537-3547.
Hassan, A. and Al-Ghamdi, A. (2009). Optimum step stress accelerated life testing for Lomax distribution. Journal of Applied Sciences Research, 5, 2153–2164.
Joshi, R. K. & Kumar, V. (2020). Lindley exponential power distribution with Properties and Applications. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(10), 22-30.
Joshi, R. K. & Kumar, V. (2020). Half Logistic NHE: Properties and Application. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(9), 742-753.
Joshi, R. K., Sapkota, L.P. & Kumar, V. (2020). The Logistic-Exponential Power Distribution with Statistical Properties and Applications, International Journal of Emerging Technologies and Innovative Research, 7(12), 629-641
Kleiber, C. (2004). Lorenz ordering of order statistics from log-Logistic and related distributions. Journal of Statistical Planning and Inference, 120, 13-19.
Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. John Wiley and Sons, Inc., Hoboken, New Jersey.
Kumar, V. (2010). Bayesian analysis of exponential extension model. J. Nat. Acad. Math, 24, 109-128.
Kumar, V. and Ligges, U. (2011). reliaR: A package for some probability distributions, http://cran.r-project.org/web/packages/reliaR/index.html.
Lan, Y., & Leemis, L. M. (2008). The logistic–exponential survival distribution. Naval Research Logistics (NRL), 55(3), 252-264.
Lee, E. T. & Wang, J. (2003). Statistical methods for survival data analysis (Vol. 476). John Wiley & Sons.
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.
Lomax, K. S. (1954). Business failures: Another example of the analysis of failure data. Journal of the American Statistical Association, 49(268), 847-852.
Mailund, T. (2017). Functional Programming in R: Advanced Statistical Programming for Data Science, Analysis and Finance. Apress, Aarhus N, Denmark ISBN-13 (pbk): 978-1-4842-2745-9 ISBN-13 (electronic): 978-1-4842-2746-6 DOI 10.1007/978-1-4842-2746-6
Mandouh, R. M. (2018). Logistic-modified weibull distribution and parameter estimation. International Journal of Contemporary Mathematical Sciences, 13(1), 11-23.
Moors, J. (1988). A quantile alternative for kurtosis. The Statistician, 37, 25-32.
R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
Smith, R.M. and Bain, L.J. (1975). An exponential power life-test distribution, Communications in Statistics, 4, 469-481
Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., & Zubair, M. (2016). The logistic-X family of distributions and its applications. Communications in Statistics-Theory and Methods, 45(24), 7326-7349.