  Mean absolute deviation function is used to explore the pattern and the
distribution of the data graphically to enable analysts gaining greater
understanding of raw data and to foster quick and a deep understanding of the
data as an important fundament for successful data analytic. Furthermore, new
nonparametric approaches for estimating the cumulative distribution function
based on the mean absolute deviation function are proposed. These new
approaches are meant to be a general nonparametric class that includes the
empirical distribution function as a special case. Simulation study reveals
that the Richardson extrapolation approach has a major improvement in terms of
average squared errors over the classical empirical estimators and has
comparable results with smooth approaches such as cubic spline and constrained
linear spline for practically small samples. The properties of the proposed
estimators are studied. Moreover, the Richardson approach applied for real data
application and used to estimate the hazardous concentration five percent.
