Abstract

In this study, we have introduced a three-parameter univariate continuous distribution called Logistic Chen distribution. Some distributional properties of the distribution such as the shapes of the probability density, cumulative distribution and hazard rate functions, quantile function, survival function, the skewness, and kurtosis measures are derived and established. To estimate the model parameters, we have employed three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. A real data set is considered to explore the applicability and capability of the proposed distribution also AIC, BIC, CAIC and HQIC are calculated to assess the potentiality of the Logistic Chen distribution.

Keywords

References

[1] Z. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49(2000) 155-161.
[2] A. K. Srivastava, and V. Kumar, Markov Chain Monte Carlo methods for Bayesian inference of the Chen model. International Journal of Computer Information Systems, 2(2) (2011) 07-14.
[3] F. A. Bhatti, G. G. Hamedani, S. M. Najibi, and M. Ahmad, On the Extended Chen Distribution: Development, Properties, Characterizations and Applications. Annals of Data Science. (2019) 1-22.
[4] B. Tarvirdizade, and M. Ahmadpour, A New Extension of Chen Distribution with Applications to Lifetime Data. Communications in Mathematics and Statistics, (2019) 1-16.
[5] R. K. Joshi, and V. Kumar, Lindley-Chen Distribution with Applications. International Journals of Engineering, Science & Mathematics (IJESM), 9(10)(2020) 12-22.
[6] A.K. Chaudhary and V. Kumar, A Study on Properties and Applications of Logistic Modified Exponential Distribution. International Journal of Latest Trends in Engineering and Technology (IJLTET), 17(5) (2020).
[7] M. H. Tahir, G. M. Cordeiro, A. Alzaatreh, M. Mansoor, and M. Zubair, The logistic-X family of distributions and its applications. Communications in Statistics-Theory and Methods, 45(24)(2016) 7326-7349.
[8] R. K. Joshi, L. P. Sapkota, and V. Kumar, The Logistic-Exponential Power Distribution with Statistical Properties and Applications, International Journal of Emerging Technologies and Innovative Research, 7(12)(2020) 629-641.
[9] A.K. Chaudhary and V. Kumar, A Study on Properties and Goodness-of- Fit of the Logistic Inverse Weibull Distribution. Global Journal of Pure and Applied Mathematics (GJPAM), 16(6)(2020) 871-889.
[10] Y. Lan, and L. M. Leemis, The logistic–exponential survival distribution. Naval Research Logistics (NRL), 55(3)(2008) 252-264.
[11] J. J. A. Moors, A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 37(1) (1988) 25-32.
[12] G. Casella, and R. L. Berger, Statistical Inference. Brooks/ Cole Publishing Company(1990) California.
[13] J. J. Swain, S. Venkatraman, and J. R. Wilson, Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29(4)(1988) 271–297.
[14] M. D. Nichols, and W. J. Padgett, A bootstrap control chart for Weibull percentiles. Quality and reliability engineering international, 22(2)(2006) 141-151.
[15] R Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2020). URL https://www.R-project.org/.
[16] E. G. Ming Hui, Learn R for applied statistics. Springer, (2019) New York.
[17] E. T. Lee, and J. Wang, Statistical methods for survival data analysis 476(2003) John Wiley & Sons.
[18] A. J. Lemonte, A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Computational Statistics & Data Analysis, 62(2013) 149-170.
[19] D. Bhati, M.A. Malik, and H.J. Vaman, Lindley–Exponential distribution: properties and applications. METRON. 73(2015) 335–357.
[20] R. D. Gupta, and D. Kundu, Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41(2)(1999) 173 - 188.
[21] R.M. Smith, and L.J. Bain, An exponential power life-test distribution, Communications in Statistics, 4(1975) 469-481.