The performance of restricted AIC for irregular histogram models

Histograms are frequently used to perform a preliminary study of data, such as finding outliers and determining the distribution's shape. It is common knowledge that choosing an appropriate number of bins is crucial to revealing the right information. It's also well known that using bins of different widths, which called unequal bin width, is preferable to using bins of equal width if the bin width is selected carefully. However this is a much difficult issue. In this research, a novel approach to AIC for histograms with unequal bin widths was proposed. We demonstrate the advantage of the suggested approach in comparison to others using both extensive Monte Carlo simulations and empirical examples.