Actuaries are interested in modeling actuarial data using loss models that can be adopted to describe risk exposure. This paper introduces a new flexible extension of the log-logistic distribution, called the extended log-logistic (Ex-LL) distribution, to model heavy-tailed insurance losses data. The Ex-LL hazard function exhibits an upside-down bathtub shape, an increasing shape, a J shape, a decreasing shape, and a reversed-J shape. We derived five important risk measures based on the Ex-LL distribution. The Ex-LL parameters were estimated using different estimation methods, and their performances were assessed using simulation results. Finally, the performance of the Ex-LL distribution was explored using two types of real data from the engineering and insurance sciences. The analyzed data illustrated that the Ex-LL distribution provided an adequate fit compared to other competing distributions such as the log-logistic, alpha-power log-logistic, transmuted log-logistic, generalized log-logistic, Marshall–Olkin log-logistic, inverse log-logistic, and Weibull generalized log-logistic distributions.

Natural computing refers to computational processes observed in nature and human-designed computing inspired by nature. In recent times, data fusion in the healthcare sector becomes a challenging issue, and it needs to be resolved. At the same time, intracerebral haemorrhage (ICH) is the injury of blood vessels on the brain cells, which is mainly liable for stroke. X-rays and computed tomography (CT) scans are widely applied for locating the haemorrhage position and size. Since manual segmentation of the CT scans by planimetry by the use of radiologists is a time-consuming process, deep learning (DL) is used to attain effective ICH diagnosis performance. This paper presents an automated intracerebral haemorrhage diagnosis using fusion-based deep learning with swarm intelligence (AICH-FDLSI) algorithm. The AICH-FDLSI model operates on four major stages namely preprocessing, image segmentation, feature extraction, and classification. To begin with, the input image is preprocessed using the median filtering (MF) technique to remove the noise present in the image. Next, the seagull optimization algorithm (SOA) with Otsu multilevel thresholding is employed for image segmentation. In addition, the fusion-based feature extraction model using the Capsule Network (CapsNet) and EfficientNet is applied to extract a useful set of features. Moreover, deer hunting optimization (DHO) algorithm is utilized for the hyperparameter optimization of the CapsNet and DenseNet models. Finally, a fuzzy support vector machine (FSVM) is applied as a classification technique to identify the different classes of ICH. A set of simulations takes place to determine the diagnostic performance of the AICH-FDLSI model using the benchmark intracranial haemorrhage data set. The experimental outcome stated that the AICH-FDLSI model has reached a proficient performance over the compared methods in a significant way.

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods.

We introduce here a new distribution called the power-modified Kies-exponential (PMKE) distribution and derive some of its mathematical properties. Its hazard function can be bathtub-shaped, increasing, or decreasing. Its parameters are estimated by seven classical methods. Further, Bayesian estimation, under square error, general entropy, and Linex loss functions are adopted to estimate the parameters. Simulation results are provided to investigate the behavior of these estimators. The estimation methods are sorted, based on partial and overall ranks, to determine the best estimation approach for the model parameters. The proposed distribution can be used to model a real-life turbocharger dataset, as compared with 24 extensions of the exponential distribution.

A novel version of the exponential Weibull distribution known as the extended exponential Weibull (ExEW) distribution is developed and examined using the Lehmann alternative II (LAII) generating technique. The new distributions basic mathematical properties are derived. The maximum likelihood estimation (MLE) technique is used to estimate the unknown parameters of the proposed distribution. The estimators’ performance is further assessed using the Monte Carlo simulation technique. Eventually, two real-world data sets are utilized to show the applicability of the new distribution.