Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 16, Number 6 (2020), pp. 871-889 © Research India Publications https://dx.doi.org/10.37622/GJPAM/16.6.2020.871-889 A Study on Properties and Goodness-of-Fit of the Logistic Inverse Weibull Distribution Arun Kumar Chaudhary 1 , Vijay Kumar 2 1 Department of Management Science(Statistics), Nepal Commerce Campus, Tribhuwan University, Kathmandu, Nepal. 2 Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur-273009, India. Abstract In this paper, we purpose a three-parameter univariate continuous distribution called Logistic Inverse Weibull Distribution. We have presented some statistical properties of the purposed distribution including the cumulative distribution function, probability density function, hazard rate function, survival function, quantile function, etc. The three well-known estimation methods namely least-square estimation (LSE), maximum likelihood estimation (MLE), and Cramer-Von-Mises estimation (CVME) methods are used for the model parameter estimation. The overall goodness of fit of the proposed distribution is assessed by comparison with some other existing distributions using a real data set. Keywords: Logistic distribution, Inverse Weibull distribution, survival function, LSE, CVME, MLE 1. INTRODUCTION The Weibull distribution has been extensively used in survival and reliability analysis. For a detailed study, the learners can go through Lai et al. (2003) and Nadarajah (2009). Even though its widespread use, it has some drawbacks that shape of its hazard rate function (HRF) are restricted that can only be monotonically constant or decreasing or increasing. Usually, real-world problems require a broader range of possibilities in the moderate risk, for instance, in the case of biological mortality and