Truncated log-logistic Family of Distributions
Abstract
Background & Aim: There are various data associated with any events in the world which need to be analyzed. In response to this, many researchers attempt to find appropriate methods that could better fit these data using new models. One of these methods is to introduce new distributions which could better describe available data. During last few years, new distributions have been extended based on existing well-known distributions. Usually, new distributions have more parameters than existing ones. This addition of parameter(s) has been proved useful in exploring tail properties and also for improving the goodness-of-fit of the family under study.
Methods & Materials: A new family of distributions is introduced by using truncated log-logistic distribution. Some statistical and reliability properties of the new family are derived.
Results: Four special lifetime models of the new family are investigated. We estimate the parameters by maximum likelihood method. The obtained results are validated using a real dataset and it is shown that the new distributions provide a better fit than some other known distributions.
Conclusion: We have provided four new distributions. The flexibility of the proposed distributions and increased range of skewness was able to fit and capture features in one real dataset much better than some competitor distributions
2. Alexander C, Cordeiro GM, Ortega EM, Sarabia JM. Generalized beta-generated distributions. Computational Statistics & Data Analysis. 2012; 56(6):1880-97.
3. Zografos K, Balakrishnan N. On families of beta-and generalized gamma-generated distributions and associated inference. Statistical Methodology. 2009; 6(4):344-62.
4. Amini M, MirMostafaee SM, Ahmadi J. Log-gamma-generated families of distributions. Statistics 2014; 48(4):913-32.
5. Ristić MM, Balakrishnan N. The gammaexponentiated exponential distribution. Journal of Statistical Computation and Simulation. 2012; 82(8):1191-206.
6. Cordeiro GM, Ortega EM, da Cunha DC. The exponentiated generalized class of distributions. Journal of Data Science. 2013; 11(1):1-27.
7.Alzaatreh A, Lee C, Famoye F. T-normal family of distributions: A new approach to generalize the normal distribution. Journal of Statistical Distributions and Applications 2014; 1(1):16.
8.Alzaghal A, Famoye F, Lee C. Exponentiated T-X Family of Distributions with Some Applications. International Journal of Statistics and Probability. 2013; 2(3):31.
9. Bourguignon M, Silva RB, Cordeiro GM. The Weibull-G family of probability distributions. Journal of Data Science. 2014; 12(1):53-68.
10. Cordeiro GM, Alizadeh M, Ortega EM. The exponentiated half-logistic family of distributions: Properties and applications. Journal of Probability and Statistics. 2014; 2014.
11. Aljarrah MA, Lee C, Famoye F. On generating TX family of distributions using quantile functions. Journal of Statistical Distributions and Applications. 2014; 1(1):2.
12.Cordeiro GM, Ortega EM, Popović BV, Pescim RR. The Lomax generator of distributions: Properties, minification process and regression model. Applied Mathematics and Computation 2014; 247:465-86.
13. Cordeiro GM, Ortega EM, Silva GO. The Kumaraswamy modified Weibull distribution: theory and applications. Journal of Statistical Computation and Simulation. 2014; 1387-411.
14. Alizadeh M, Emadi M, Doostparast M, Cordeiro GM, Ortega EM, Pescim RR. A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepe Journal of Mathematics and Statistics. 2015; 44(6):1491-512.
15. Tahir MH, Cordeiro GM, Alzaatreh A, Mansoor M, Zubair M. The Logistic-X family of distributions and its applications. Communications in Statistics-Theory and Methods. 2016; 45(24):7326-49.
16. Mahdavi A, Kundu D. A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods. 2017; 46(13):6543-57.
17. Mahdavi A, Oliveira Silva G. A Method to Expand Family of Continuous Distributions based on Truncated Distributions. Journal of Statistical Research of Iran JSRI. 2017; 13(2):231-47.
18. Gupta RD, Kundu D. Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics 1999; 41(2):173-88.
19. Team RC. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2017.
20. Bjerkedal T. Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle Bacilli. American Journal of Hygiene. 1960; 72(1):130-48.
21. Gupta RD, Kundu D. A new class of weighted exponential distributions. Statistics. 2009; 43(6):621-34.
| Files | ||
| Issue | Vol 5 No 2 (2019) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/jbe.v5i2.2345 | |
| Keywords | ||
| Hazard rate function Log-logistic distribution Maximum-likelihood estimation Survival reliability function | ||
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