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Lecture15-2010

# 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. Definition : Two cummulative distributions functions G 1 ( . ) and G 2 ( . ) are said to di ff er only by location and scale parameters and if G 1 ( x ) = G 2 ( α + β x ) 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 di ff er 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 ] = b a u ( μ i + σ i x ) dF ( x ) V ( σ i , μ i ) (2) E. The first step in examining the properties of V ( σ , μ ) is to examine its partial derivatives V σ ( σ , μ ) = b a u ( μ + σ x ) xdF ( x ) = b a u ( μ + σ x ) x a xdF ( x ) dx V μ ( σ , μ ) = b a u ( μ + σ x ) dF ( x ) (3) 1

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AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture XV Fall 2010 1. Property 1 : V μ ( σ , μ ) > 0 for all μ and all σ > 0 if and only if u ( α + β x ) 0 for all α + β x .
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Lecture15-2010 - Meyers Location Scale Lecture XV Charles B...

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