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Activity Number:
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353
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Type:
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Contributed
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Date/Time:
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Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistics & the Environment*
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| Abstract - #301010 |
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Title:
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Properties and Applications of Power Normal Distribution
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Author(s):
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Reza Modarres*+ and Jade Freeman
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Affiliation(s):
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George Washington University and U.S. Environmental Protection Agency
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Address:
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2201 G st. NW, Washington DC, District of Columbia, 20052, usa
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Keywords:
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Box-Cox Transformation ; Skewed Distributions ; Power Normal Family
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Abstract:
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The Box-Cox translation system produces the Power Normal (PN) family of distributions, which include normal and lognormal as members. This transformation has proved useful when dealing with skewed environmental data. Whenever an effective Box-Cox transformation can be established, one can argue that the observations in the original scale must be well-approximated by a member of the PN family. We study the moments of PN and obtain expressions for the mean vector and the covariance matrix for specified vector of power transformations (PT). Chevyshev-Hermite polynomials are used to obtain expressions for the moments in the original scale for integer values of the PT. Using an expression for the correlation in the untransformed scale, we show that the correlation of coefficient in the transformed scale is generally smaller than the same value in the untransformed scale. We study the conditional distributions and show that they are also in the PN family. We use the Fre'chet bounds to obtain expressions for the lower and upper bounds of the correlation for selected vector of PTs. We obtain expressions for the univariate quantile functions and use them to describe the behavior of the order.
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