A KURTOSIS MEASURE FOR HEAVY TAIL SYMMETRIC DENSITIES

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FARNOOSH RAHMAN; JAFARPOUR HEDIEH

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ISSN: 2588-4824

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Journal: JOURNAL OF MATHEMATICAL EXTENSION Year:2006 | Volume:1 | Issue:1 Page(s): 1-14

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Title

A KURTOSIS MEASURE FOR HEAVY TAIL SYMMETRIC DENSITIES

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FARNOOSH RAHMAN | JAFARPOUR HEDIEH | Issue Writer Certificate

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Abstract

The usual kurtosis measure, forth central moment divided by second central moment, does not measure only peaked ness of distribution with respect to normal distribution. But it measures both peaked ness and tail weight of distributions. In this paper we consider some disadvantages of the kurtosis measure. It can be misleading as a measure of departure from normality. This measure does not work well for some families, for example Ali's scale contaminated normal distribution. It is infinite for heavy tail distribution. In other words it is so sensitive to extreme values. We introduce a modified of kurtosis which is robust against the extreme values. We name the kurtosis measure by bqp (F). Properties of the introduced measure are as the same as usual kurtosis measure. By using this measure and Van Zwet’s ordering we can sort distributions based on heaviness or peaked ness separately. Finally by Monte Carlo simulation we find the critical values at some levels for the measure.

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APA: Copy

FARNOOSH, RAHMAN, & JAFARPOUR, HEDIEH. (2006). A KURTOSIS MEASURE FOR HEAVY TAIL SYMMETRIC DENSITIES. JOURNAL OF MATHEMATICAL EXTENSION, 1(1), 1-14. SID. https://sid.ir/paper/240015/en

Vancouver: Copy

FARNOOSH RAHMAN, JAFARPOUR HEDIEH. A KURTOSIS MEASURE FOR HEAVY TAIL SYMMETRIC DENSITIES. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2006;1(1):1-14. Available from: https://sid.ir/paper/240015/en

IEEE: Copy

RAHMAN FARNOOSH, and HEDIEH JAFARPOUR, “A KURTOSIS MEASURE FOR HEAVY TAIL SYMMETRIC DENSITIES,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 1, no. 1, pp. 1–14, 2006, [Online]. Available: https://sid.ir/paper/240015/en

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