Lecture15-2010 - Meyers Location Scale Lecture XV Charles B...

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Meyer’s Location Scale: Lecture XV Charles B. Moss September 26, 2010 I. Meyers Location-Scale A. Defnition : Two cummulative distributions functions G 1 ( . )and G 2 ( . ) are said to diFer only by location and scale parameters and if G 1 ( x )= G 2 ( α + βx ) with β> 0. B. Several two-parameter families satisfy this property such as the normal and the uniform distributions. C. Assume that there exists various choice sets, Y i , that only diFer by location and scale parameters. X i = Y i μ i σ i (1) D. The expected utility of this alternative can then be derived as E U [ Y i ]= Z b a u ( μ i + σ i x ) dF ( x ) V ( σ i i ) (2) E. The ±rst step in examining the properties of V ( σ, μ )istoexamine its partial derivatives V σ ( σ, μ )= Z b a u 0 ( μ + σx ) xdF ( x ) = Z b a ± u 0 ( μ + σx ) Z x a xdF ( x ) ² dx V μ ( σ, μ )= Z b a u 0 ( μ + σx ) dF ( x ) (3) 1
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AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture XV
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This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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Lecture15-2010 - Meyers Location Scale Lecture XV Charles B...

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