Ad-p lot and Ud-plot for determining distributional characteristics and normality

The histogram and boxplot are broadly used to visualize distributional characteristics of the data such as symmetry, skewness, and outliers. Sv-plot1, Sv-plot2, and Sv-plot3 can also detect these attributes, and remarkably, Sv-plot2 and Sv-plot3 are employable in testing hypotheses. Meanwhile, normal QQ-plot and normal PP-plot are leading tools for assessing normality. Herein two statistical plots, Ad-plot and Ud-plot are innovated by investigating a novel functional estimator that is formed by cumulatively averaging the deviations of the data below a target value. The Ad-plot can depict symmetry, skewness, and outliers of the distribution as histogram and Sv-plot2 reveal. Concurrently, the Ud-plot derived from a slight modification of the estimator by proving a theorem helps visualize normality analogous to normal QQ- and PP-plots. The d-value is introduced by quantifying the degree of proximity of the Ud-plot to the graph of the estimated normal probability density function. Ud-plot accompanied by the desirable normal curve greatly enhances the perception on checking normality. The simulated and real data strongly agree with the Ad-plot for identifying central distributional characteristics competing with sv-plot2 and histogram. Exceptionally, the Ud-plot is prominent in assessing normality by delivering an informative value-added data visualization, outperforming both normal QQ-plot and normal PP-plot.