Empirical Cumulative Distribution Function as an Informative Tool-ECO6416

# Empirical Cumulative Distribution Function as an Informative Tool-ECO6416

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Empirical Cumulative Distribution Function as an Informative Tool Interquartiles Range: The interquartile range (IQR) describes the extent for which the middle 50% of the observations scattered or dispersed. It is the distance between the first and the third quartiles: IQR = Q3 - Q1, which is twice the Quartile Deviation. For data that are skewed , the relative dispersion , similar to the coefficient of variation (C.V.) is given (provided the denominator is not zero) by the Coefficient of Quartile Variation: CQV = (Q3-Q1) / (Q3 + Q1). Note that almost all statistics that we have covered up to now can be obtained and understood deeply by graphical method using Empirical (i.e., observed) Cumulative Distribution Function (ECDF) JavaScript. However, the numerical Descriptive Statistics provides a complete set of information about all statistics that you ever need. The Duality between the ECDF and the Histogram: Notice that the empirical (i.e., observed) cumulative distribution function ( ECDF ) indicates by its height at a particular pointthat is numerically equal to the area in the corresponding histogram to the left of that point. Therefore, either or both could be used depending on the intended applications. Mean Absolute Deviation (MAD): A simple measure of variability is the mean absolute deviation: MAD = Σ |(x i - )| / n. The mean absolute deviation is widely used as a performance measure to assess the quality of the modeling, such forecasting techniques . However, MAD does not lend itself to further use in making inference; moreover, even in the error analysis studies, the variance is preferred since variances of independent (i.e., uncorrelated) errors are additive; however MAD does not have such a nice feature. The MAD is a simple measure of variability, which unlike range and quartile deviation, takes every item into account, and it is simpler and less affected by extreme deviations. It is therefore often used in small samples that include extreme values. The mean absolute deviation theoretically should be measured from the median, since it is at its minimum; however, it is more convenient to measure the deviations from the mean. As a numerical example, consider the price (in \$) of same item at 5 different stores: \$4.75, \$5.00, \$4.65, \$6.10, and \$6.30. The mean absolute deviation from the mean is \$0.67, while from the median is \$0.60, which is a better representative of deviation among the prices. Variance:

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Empirical Cumulative Distribution Function as an Informative Tool-ECO6416

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