STATISTICAL INFERENCES OF GROUPED DATA COMBINED WITH UNGROUPED DATA FROM THE POWER-NORMAL DISTRIBUTION

We describe an exploratory approach to analyzing grouped data in which an underlying distribution of data is unknown or there is no strong knowledge of the process of generating the data. In addition to the most elementary situation where one variable of interest and its observations are given in a grouped form such as a frequency table, we consider the two types of mixed grouped data, I.e., ungrouped data available in the tail and right and/or left censored data. We develop the procedure of the parameter estimation and investigate the asymptotic properties of the estimates for each type of grouped data. We also provide two examples to illustrate the proposed approach. The results show that the proposed approach would help to "regularize" the data even when it does not yield normality.