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Unformatted text preview: a. The inverse Gaussian distribution with density f y ( y ; , ) = (2 y 3 / )1 / 2 exp { 2 2 ( y ) 2 /y } , y,, > . b. The Pareto distribution with density f y ( y ; ) = a /y ( +1) , y > a, > ,a > 2. Determine whether the following distributions belong to the ED family. If not, is there a transformation of the random variable Y which does have an ED distribution? a. The extreme value (Gumbel) distribution with density f Y ( y ; , ) = 1 exp { ( y )exp[( y ) / ] } b. The lognormal distribution with density f Y ( y ; , ) = 1 y 2 exp {1 2 (log y ) 2 } 3. For the classical linear model y = X + , where y , are n vectors, has dimension p , X is n p , and the i s are i.i.d. N (0 , 2 ), show that the information matrix of is 2 X T X . 48. Problems 4.2, 4.19, 4.22, 4.23, 4.29 in Agresti....
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 Fall '11
 Hall
 Statistics

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