Background: In diabetic retinopathy (DR) screening programmes feature-based grading guidelines are used by human graders. However, recent deep learning approaches have focused on end to end learning, based on labelled data at the whole image level. Most predictions from such software offer a direct grading output without information about the retinal features responsible for the grade. In this work, we demonstrate a feature based retinal image analysis system, which aims to support flexible grading and monitor progression. Methods: The system was evaluated against images that had been graded according to two different grading systems; The International Clinical Diabetic Retinopathy and Diabetic Macular Oedema Severity Scale and the UK’s National Screening Committee guidelines. Results: External evaluation on large datasets collected from three nations (Kenya, Saudi Arabia and China) was carried out. On a DR referable level, sensitivity did not vary significantly between different DR grading schemes (91.2–94.2.0%) and there were excellent specificity values above 93% in all image sets. More importantly, no cases of severe non-proliferative DR, proliferative DR or DMO were missed. Conclusions: We demonstrate the potential of an AI feature-based DR grading system that is not constrained to any specific grading scheme.

The cubic transformation families of distributions are widely used to model complex univariate data. However, in many situations, the jointly modeling of two variables is necessary, making bivariate distributions essential. This paper introduces a novel family of bivariate probability distributions that extends the univariate cubic transformation family. The bivariate cubic transmuted (BCT) family of distributions is comprehensively discussed, with its statistical properties explored in detail. Within this family, the bivariate cubic transmuted Burr (BCTB) distribution is specifically analyzed. Its statistical properties are examined, and its parameters are estimated using the maximum likelihood estimation (MLE) method. To assess the performance of the estimation procedure, a Monte Carlo simulation study is conducted. Furthermore, the applicability of the proposed model is demonstrated by fitting it to real datasets, and its relevance is further discussed.

The modeling of complex data has attracted several researchers for the quest of generating new probability distributions. The joint modeling of two variables asks for some additional complexities as a bivariate distribution is needed. The field of research in developing bivariate families of distributions is somewhat new. In certain situations, the domain of data is restricted and some truncated distribution is required. Several univariate truncated families of distributions are available for modeling of a single variable but the bivariate truncated families of distributions has not been studied and in this paper, we have proposed a new bivariate truncated families of distributions. A specific sub-family has been proposed by using the bivariate Burr as a base-line distribution, resulting in a bivariate truncated Burr family of distributions. Some important statistical properties of the proposed family has been studied, which include the marginal and conditional distributions, bivariate reliability, and bivariate hazard rate functions. The maximum likelihood estimation for the parameters of the family is also carried out. The proposed bivariate truncated Burr family of distributions is studied for the Burr baseline distributions, giving rise to the bivariate truncated Burr-Burr distribution. The new bivariate truncated Burr-Burr distribution is explored in detail and several statistical properties of the new distribution are studied, which include the marginal and conditional distributions, product, ratio, and conditional moments. The maximum likelihood estimation for the parameters of the proposed distribution is done. The proposed bivariate truncated Burr-Burr distribution is used to model some real data sets. It is found that the proposed distribution performs better than the other distributions considered in this study.

The modeling of complex data has garnered significant interest among researchers, leading to the development of novel probability distributions. Joint modeling of two variables introduces additional challenges, necessitating the use of bivariate distributions. The field of bivariate distribution development remains relatively nascent, particularly for truncated distributions, which are essential in situations where data domains are restricted. While univariate truncated distributions have been extensively studied, their bivariate counterparts remain largely unexplored. In this paper, we propose a new bivariate distribution, termed the Bivariate Truncated Burr–Weibull (BTB-W) distribution, and investigate its statistical properties in detail. These include the marginal and conditional distributions, product and ratio moments, and conditional moments. Parameter estimation is performed using maximum likelihood techniques. The proposed BTB-W distribution is evaluated against established models, including the bivariate Burr, bivariate Lomax, bivariate log-logistic, and bivariate transmuted Weibull distributions, using real datasets. The comparative analysis, based on Akaike Information Criterion (AIC) and Bayesian Information Criterion, demonstrates that the BTB-W distribution outperforms the competing models, establishing its effectiveness and utility in complex data modeling.