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Unformatted text preview: a. The inverse Gaussian distribution with density f y ( y ; Î¼,Î» ) = (2 Ï€y 3 /Î» )1 / 2 exp {Î» 2 Î¼ 2 ( yÎ¼ ) 2 /y } , y,Î»,Î¼ > . b. The Pareto distribution with density f y ( y ; Î¸ ) = Î¸a Î¸ /y ( Î¸ +1) , y > a,Î¸ > ,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 ; Î¸,Ï† ) = 1 Ï† exp { ( yÎ¸ Ï† )exp[( yÎ¸ ) /Ï† ] } b. The lognormal distribution with density f Y ( y ; Î¸,Ï† ) = 1 y âˆš 2 Ï€Ï† exp {1 2 Ï† (log yÎ¸ ) 2 } 3. For the classical linear model y = X Î² + Îµ , where y , Îµ are n vectors, Î² has dimension p , X is n Ã— p , and the Îµ i â€™s are i.i.d. N (0 ,Ïƒ 2 ), show that the information matrix of Î² is Ïƒ2 X T X . 4â€“8. Problems 4.2, 4.19, 4.22, 4.23, 4.29 in Agresti....
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This note was uploaded on 11/13/2011 for the course STAT 8620 taught by Professor Hall during the Fall '11 term at University of Florida.
 Fall '11
 Hall
 Statistics

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