Modi-Weibull Distribution: Inferential and Simulation Study

This paper presents a study on a new family of distributions using the Weibull distribution and termed as Modi-Weibull distribution. This Modi-Weibull distribution is based on four parameters. To understand the behaviour of the distribution, some statistical characteristics have been derived, such as shapes of density and distribution function, hazard function, survival function, median, moments, order statistics etc. These parameters are estimated using classical maximum likelihood estimation method. Asymptotic confidence intervals for parameters of Modi-Weibull distribution are also obtained. A simulation study is carried out to investigate the bias, MSE of proposed maximum likelihood estimators along with coverage probability and average width of confidence intervals of parameters. Two applications to real data sets are discussed to illustrate the fitting of the proposed distribution and compared with some well-known distributions. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.