# On Uses of Mean Absolute Deviation: Shape Exploring and Distribution Function Estimation

@inproceedings{Elamir2022OnUO, title={On Uses of Mean Absolute Deviation: Shape Exploring and Distribution Function Estimation}, author={Elsayed A. H. Elamir}, year={2022} }

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 nonparametricβ¦Β

## References

SHOWING 1-10 OF 47 REFERENCES

### On uses of mean absolute deviation: decomposition, skewness and correlation coefficients

- Mathematics
- 2012

SummaryThe mean absolute deviation about mean is expressed as a covariance between a random variable and its under/over indicator functions. Based on this representation new correlation coefficientsβ¦

### EXACT MEAN INTEGRATED SQUARED ERROR

- Mathematics
- 1992

An exact and easily computable expression for the mean integrated squared error (MISE) for the kernel estimator of a general normal mixture density, is given for Gaussian kernels of arbitrary order.β¦

### REGRESSION MODELING FOR NONPARAMETRIC ESTIMATION OF DISTRIBUTION AND QUANTILE FUNCTIONS

- Mathematics
- 2002

We propose a local linear estimator of a smooth distribution function. This estimator applies local linear techniques to observations from a regression model in which the value of the empiricalβ¦

### Distribution function estimation by constrained polynomial spline regression

- Mathematics
- 2010

A smooth monotone polynomial spline (PS) estimator is proposed for the cumulative distribution function. The proposed method applies a constrained PS regression to smooth the empirical distributionβ¦

### Application of Bernstein Polynomials for smooth estimation of a distribution and density function

- Mathematics
- 2002

### Second Order Efficient Estimating a Smooth Distribution Function and its Applications

- Mathematics
- 2001

Consider a problem of estimation of a cumulative distribution function of a random variable supported on a finite interval, with a circular random variable being a particular case. It is well knownβ¦

### Nonparametric Estimation of a Cdf with Mixtures of Cdf Concentrated on Small Intervals

- Mathematics
- 2006

In this paper, we propose a new nonparametric approach for estimating a cumulative distribution function F using finite mixtures. This new approach is meant to be an alternative to classical methodsβ¦

### Kernel Estimation of Cumulative Distribution Function of a Random Variable with Bounded Support

- Mathematics
- 2016

Abstract In the paper methods of reducing the so-called boundary effects, which appear in the estimation of certain functional characteristics of a random variable with bounded support, areβ¦

### An alternative distribution function estimation method using rational Bernstein polynomials

- MathematicsJ. Comput. Appl. Math.
- 2019