Research Article
On Some Alternative Probability Density Metrics for Analyzing Empirical Datasets
@INPROCEEDINGS{10.1007/978-3-031-44668-9_3, author={Sidney Klawansky and Brielle Balswick and Meaad Alsayel and Iryna Charvachidze and Anuka Manghwani and Pearl Almeida and Dharmit Dalvi and Janvi Vora and Eugene Pinsky}, title={On Some Alternative Probability Density Metrics for Analyzing Empirical Datasets}, proceedings={Computer Science and Education in Computer Science. 19th EAI International Conference, CSECS 2023, Boston, MA, USA, June 28--29, 2023, Proceedings}, proceedings_a={CSECS}, year={2023}, month={10}, keywords={mean absolute deviation skewness asymmetry kurtosis tailness}, doi={10.1007/978-3-031-44668-9_3} }- Sidney Klawansky
Brielle Balswick
Meaad Alsayel
Iryna Charvachidze
Anuka Manghwani
Pearl Almeida
Dharmit Dalvi
Janvi Vora
Eugene Pinsky
Year: 2023
On Some Alternative Probability Density Metrics for Analyzing Empirical Datasets
CSECS
Springer
DOI: 10.1007/978-3-031-44668-9_3
Abstract
We propose a simple set of probability density shape metrics with intuitive interpretability and complement the Classical statistical metrics of Variance, Skewness, and Kurtosis. These Classical metrics involve squaring of deviations and computation of third and fourth moments. Therefore, they may be overly sensitive to outliers. Therefore, we take The Mean Deviation around the mean, rather than the standard deviation, as the primary measure of data dispersion. This work presents some of our initial results using Mean Deviation and the new metrics of Tailness (an analog of Kurtosis) and Asymmetry (an analog of Skewness). These new metrics use only first and second moments. They have simple interpretations and directly allow us to compare datasets with different measurement units. As such, they give us additional tools for data analysis. We illustrate the proposed metrics for several public datasets.
