Regarding the Novel IDNAII Distribution: Mathematical and Statistical Characteristics

<ns3:p>Over the last decade, there has been an increased range of probability distributions in statistical and reliability literature aimed at enhancing standard models. This trend reflects a greater understanding of empirical integrity, flexibility, and adaptability in modeling income distributions, reliability, and lifetime statistics. To provide greater flexibility and general distributions, this study employs a technique that generates the T−R{Y} family distributions. It might be employed to agree with particular forms of data distributions, including the significantly left, right, thin, or heavy-tailed distributions, or for creating new distributions that are very flexible and adaptive. These results in an individual belonging to a new sub-family called the IDNAII distribution, which is also referred to as the Lomax–Weibull {Exponential} distribution. The main statistical and mathematical aspects of the new family distribution are examined. A variety of estimation approaches, including the maximum likelihood method (MLE), method of moments (MOM), least squares method (LS), and shrinkage method (SH), will be introduced to estimate the parameters of the new class distribution. Simulation tools have been created to evaluate the effectiveness of estimation approaches. The study’s findings indicate that the shrinkage estimation approach exceeded the others regarding bias and mean squared error criterion. On the contrary, a real-world dataset application has been demonstrated and the examination of the real dataset showed that the new class distribution fit the data better than the particular classical and moderate distributions, as indicated by several types of information criteria.</ns3:p>