## THERMAL SCIENCE

International Scientific Journal

### COMPARISONS OF SIX DIFFERENT ESTIMATION METHODS FOR LOG-KUMARASWAMY DISTRIBUTION

**ABSTRACT**

In this paper, it is considered the problem of estimation of unknown parameters of log-Kumaraswamy distribution via Monte Carlo simulations. Firstly, it is described six different estimation methods such as maximum likelihood, approximate bayesian, least-squares, weighted least-squares, percentile and Crámer-von-Mises. Then, it is performed a Monte Carlo simulation study to evaluate the performances of these methods according to the biases and mean-squared errors (MSEs) of the estimators. Furthermore, two real data applications based on carbon fibers and the gauge lengths are presented to compare the fits of log-Kumaraswamy and other fitted statistical distributions.

**KEYWORDS**

PAPER SUBMITTED: 2019-04-11

PAPER REVISED: 2019-07-25

PAPER ACCEPTED: 2019-08-01

PUBLISHED ONLINE: 2019-09-15

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 6**, PAGES [S1839 - S1847]

- Lemonte, A. J., et al., The exponentiated Kumaraswamy distribution and its log-transform, Brazilian Journal of Probability and Statistics, 27 (2013), 1, pp. 31-53
- Kumaraswamy, P., A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46 (1980), 1-2, pp. 79-88
- Mohammed, H. F., Inference on the Log-Exponentiated Kumaraswamy Distribution. International Journal of Contemporary Mathematical Sciences, 12 (2017), 4, pp. 165-179
- Chacko, M., Mohan, R., Estimation of parameters of Kumaraswamy-exponential distribution under progressive type-II censoring. Journal of Statistical Computation and Simulation, 87 (2017), 10, pp. 1951-1963
- Akinsete, A, et al., The Kumaraswamy-geometric distribution.Journal of Statistical Distributions and applications. (2014), pp.1-17
- Jose, K. K., Varghese, J., Wrapped Log Kumaraswamy Distribution and its Applications. International Journal Of Mathematics And Computer Research, 6 (2018), 10, pp. 1924-1930
- Korkmaz, M. Ç., Genç, A. İ.., Two-sided generalized exponential distribution. Communications in Statistics-Theory and Methods, 44, (2015), 23, pp.5049-5070
- Korkmaz, M. Ç., Genc, A. İ. A lifetime distribution based on a transformation of a two-sided power variate. Journal of Statistical Theory and Applications, 14 (2015), 3, pp.265-280.
- Ramos, P. L., Louzada, F., The generalized weighted Lindley distribution: Properties, estimation, and applications. Cogent Mathematics, 3 (2016), 1, 1256022.
- Dey, S et al., Comparisons of Methods of Estimation for the NH Distribution. Annals of Data Science, 4 (2017), 4, pp. 441-455.
- Dey, S., et al., Kumaraswamy distribution: different methods of estimation. Computational and Applied Mathematics, 37 (2018), 2, pp. 2094-2111
- Dey, S., et al., Statistical properties and different methods of estimation of Gompertz distribution with application. Journal of Statistics and Management Systems, 21 (2018), 5, pp. 839-876.
- Ramos, P. et al., (2018). The Frechet distribution: Estimation and Application an Overview. arXiv preprint arXiv:1801.05327.
- Balakrishnan, N., Kundu, D., Birnbaum‐Saunders distribution: A review of models, analysis, and applications. Applied Stochastic Models in Business and Industry, 35 (2019), 1, pp.4-49
- Tierney, L., Kadane, J. B., Accurate approximations for posterior moments and marginal densities. Journal of the american statistical association, 81 (1986), 393, pp. 82-86
- Danish, M. Y., Aslam, M., Bayesian estimation for randomly censored generalized exponential distribution under asymmetric loss functions. Journal of Applied Statistics, 40 (2013), 5, pp. 1106-1119
- Gencer, G., Saracoglu, B., Comparison of approximate Bayes Estimators under different loss functions for parameters of Odd Weibull Distribution. Journal of Selcuk University Natural and Applied Science, 5 (2016), 1, pp. 18-32
- Kumar, K., Classical and Bayesian estimation in log-logistic distribution under random censoring. International Journal of System Assurance Engineering and Management, 9 (2018), 2, pp. 440-451
- Kınacı, et al., Kesikli Chen Dağılımı için Bayes Tahmini. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, 42 (2016), 2, pp. 144-148
- Tanış, C., Saraçoğlu, B.,. Statistical Inference Based on Upper Record Values for the Transmuted Weibull Distribution, International Journal of Mathematics and Statistics Invention, 5 (2017), 9, pp. 19-23
- Jung, M., Chung, Y., Bayesian inference of three-parameter bathtub-shaped lifetime distribution. Communications in Statistics-Theory and Methods, 47 (2018), 17, pp. 4229-4241
- Kao JHK., Computer methods for estimatingWeibull parameters in reliability studies. Trans IRE Reliab Qual Control, 13 (1958), pp.15-22
- Kao JHK., A graphical estimation of mixed Weibull parameters in life testing electron tubes Technometrics, 1 (1959), pp. 389-407
- Gupta R. D., Kundu D., Generalized exponential distribution: different method of estimations. Journal of Statistical Computation and Simulation, 69 (2001), pp. 315-338
- Alkasabeh MR, Raqab MZ, Estimation of the generalized logistic distribution parameters: comparative study. Statistical Methodology, 6 (2009), 3, pp. 262-279
- Erisoglu, U., Erisoglu, M., Percentile Estimators for Two-Component Mixture Distribution Models. Iranian Journal of Science and Technology, Transactions A: Science, 43 (2019) 2, pp. 601-619
- Luceño, A., Fitting the generalized pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics & Data Analysis, 51 (2006), pp. 904-917
- Macdonald, P., An estimation procedure for mixtures of distribution. Journal of the Royal Statistical Society. Series B (Methodological), 33 (1971), pp.326-329
- Bader, M. G., & Priest, A. M., Statistical aspects of fibre and bundle strength in hybrid composites. Progress in science and engineering of composites, (1982), pp.1129-1136.
- Kundu, D., Raqab, M. Z., Estimation of R= P (Y< X) for three-parameter Weibull distribution. Statistics & Probability Letters, 79, (2009), 17, pp. 1839-1846
- Ghitany, M. E., et al., Power Lindley distribution and associated inference. Computational Statistics & Data Analysis, 64, (2013), pp. 20-33
- Nofal, Z. M., et al., The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Methods, 46, (2017), 8, pp. 4119-4136
- Nichols, M. D., Padgett, W. J., A bootstrap control chart for Weibull percentiles. Quality and reliability engineering international, 22, (2006), 2, pp. 141-151