Heavy tailed distributions play very significant role in the study of actuarial and financial risk management data but the probability distributions proposed to model such data are scanty. Actuaries often search for new and appropriate statistical models to address data related to financial risk problems. In this work, we propose a new family of heavy tailed distributions. Some basic properties of this new family of heavy tailed distributions are obtained. A special sub-model of the proposed family, called a new heavy tailed Weibull model is considered in detail. The maximum likelihood estimators of the model parameters are obtained. A Monte Carlo simulation study is carried out to evaluate the performance of these estimators. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is done. Finally, an application of the proposed model to a heavy tailed insurance loss data set is presented.

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.

For enhancing the quality and productivity, the use of process capability index (PCI) has become significant in statistical process control, designed to quantify the relation between the actual performance of the process and its specified requirements. Confidence interval is an important part of PCI because it is an estimated value and provides much more information about the population characteristic of interest than does a point estimate. In this article, bootstrap confidence intervals of non-normal PCI , is studied through simulation when the underlying distribution is exponential power distribution. Maximum likelihood method is used to estimate the parameters of the model. Four (parametric as well as non-parametric) bootstrap confidence intervals, namely standard bootstrap (s-boot), percentile bootstrap (p-boot), Student’s t bootstrap (t-boot), and bias-corrected percentile bootstrap ( -boot), are considered for obtaining confidence intervals of . A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals. Simulation results showed that among these (s-boot, p-boot, t-boot, and -boot) confidence intervals, the performances of the s-boot confidence intervals is the best in terms of overage probabilities. Finally, three real data-sets are analyzed for illustrative purposes.