A prior information-based estimation method for fitting pearson distributions: Applications in process capability and bounded data studies

The distributions to fit the data set using the moments are called the Pearson distribution family. This study proposes a novel alternative to the method of moments, which is based on some prior information (namely the lower limit, the upper limit, and the mode) about the data. In the proposed method, a theoretical distribution can be fitted with only the first moment of the data without the need for a higher-order moment if we have the limit information. The method is exemplified in a process capability context. The tolerance information provided by the customer can be used as prior information in the proposed method. An increasingly significant sub-branch of capability indices studies involves creating process capability indices for one-sided asymmetric tolerances. Using the upper and lower specification limits and the target value information provided by the customer, an acceptable process distribution can be defined as the base distribution by the proposed method and the process capability index can be calculated.