The Sine-Alpha Power A Distribution: Properties, Estimation Methods, and Applications with Change Point

Statistical distributions are essential for modeling and analyzing data in real-world situations. In parametric statistical modeling, it is critical to create generalizations of existing statistical distributions that exhibit greater flexibility for modeling real datasets. This paper presents a novel lifetime two-parameter model called the sine-alpha power A distribution (SAPAD), which is formulated by integrating the sine-alpha power-G family of distributions with the A distribution. The statistical aspects of the distribution, including the expansion of the density function, hazard functions, quantile function, moments, and characteristic function, Rényi entropy, and order statistics, are derived. Various estimation techniques have been applied to estimate the unknown parameters, and the efficiency of these estimators is examined via simulation studies. The effectiveness of the SAPAD model is demonstrated by analyzing three real-world datasets, each of which it fits more accurately than certain competing models. Furthermore, the modified information criterion (MIC) is used to illustrate the change point for the SAPAD model to detect changes in the structures of these data. Through MIC and curve analyses, a possible change point was identified, thereby validating the efficacy of the SAPAD distribution in characterizing transitions.