{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Shape of a Distribution Function-ECO6416

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online