Shape of a Distribution Function-ECO6416

Shape of a Distribution Function-ECO6416 - Shape of a...

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Shape of a Distribution Function: The Skewness-Kurtosis Chart The pair of statistical measures, skewness and kurtosis, are measuring tools, which is used in selecting a distribution(s) to fit your data. To make an inference with respect to the population distribution, you may first compute skewness and kurtosis from your random sample from the entire population. Then, locating a point with these coordinates on the widely used skewness- kurtosis chart , guess a couple of possible distributions to fit your data. Finally, you might use the goodness-of-fit test to rigorously come up with the best candidate fitting your data. Removing outliers improves the accuracy of both skewness and kurtosis. Skewness: Skewness is a measure of the degree to which the sample population deviates from symmetry with the mean at the center. Skewness = Σ (x i - ) 3 / [ (n - 1) S 3 ], n is at least 2. Skewness will take on a value of zero when the distribution is a symmetrical curve. A positive value indicates the observations are clustered more to the left of the mean with most of the extreme values to the right of the mean. A negative skewness indicates clustering to the right. In this case we have: Mean Median Mode. The reverse order holds for the observations with positive skewness. Kurtosis: Kurtosis is a measure of the relative peakedness of the curve defined by the distribution of the observations. Kurtosis = Σ (x i - ) 4 / [ (n - 1) S 4 ], n is at least 2. Standard normal distribution has kurtosis of +3. A kurtosis larger than 3 indicates the distribution is more peaked than the standard normal distribution. Coefficient of Excess Kurtosis = Kurtosis - 3.
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This note was uploaded on 10/03/2011 for the course ECO 6416 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Shape of a Distribution Function-ECO6416 - Shape of a...

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