A Novel Flexible Logarithmic Cosine-G Family of Distributions with Applications to Event Time Data

Abstract

Many probability distributions have been developed in the literature on distribution theory to describe and forecast real-world phenomena, especially in the domains of engineering, sports, and medicine. To give the current distribution greater flexibility, these distributions are generated with the addition of one or more extra parameters. Reparameterization and estimation issues are the two major issues that arise when additional parameters are added to the existing distribution. We make a significant attempt to propose a novel statistical methodological strategy for generating more flexible distributions devoid of extra parameters to prevent the aforementioned two issues. The logarithmic and cosine functions are used to build the recently described approach. A Novel Flexible Logarithmic Cosine-G (NFLC-G) family of distributions is the name given to the newly suggested approach. Additionally, some distributional characteristics of the NFLC-G family are also obtained. Using the newly suggested approach, a unique sub-model known as the Novel Flexible Logarithmic Cosine Weibull (NFLC-Wei) distribution is established. The Maximum Likelihood estimation method is used to estimate the model parameters of the proposed family of distributions. Similarly, a comprehensive Monte Carlo simulation analysis verifies the accuracy of the parameter estimation technique. From simulation analysis, it is observed that as the sample size increases, the biases and mean square errors declined as well as MLEs gradually approach the true parameter values. Moreover, three sets of biomedical data are demonstrated to check the applicability of the NFLC-G family of distributions. Using statistical information criteria, the performance of the proposed distribution is compared to other well-known existing distributions. Finally, we found that the NFLC-Wei distribution appears to be the best option for the studied data sets based on these statistical information requirements.