- 54 Exponential Family And Generalized Linear Models Poisson M Nt 100 Binomial N 1 Bernoulli Po U Bin N 7 X X B 1 (123.06 KiB) Viewed 107 times
54 EXPONENTIAL FAMILY AND GENERALIZED LINEAR MODELS Poisson M=NT 100 Binomial n=1 Bernoulli Po(u) Bin( n. 7) X,+...+X, B(7) u=r(1-0) 0²=M u=ht 02=n7 (1-70) INTT>5,07(1-71)>5 r00 u>15 Negative Binomial Normal NBin(1,0) N(1,0) u=a/B 02=a/B2) 000 Standard Uniform Gamma Exponential-OlogX G(a,b) U(0,1) a=0 B=1 Exp(0) Figure 3.3 Some relationships among distributions in the exponential family. Dotted lines indicate an asymptotic relationship and solid lines a transformation. a. Show that the Exponential distribution Exp() is a special case of the Gamma distribution Ga,ß). b. If X has the Uniform distribution U[0, 1], that is, f(x) = 1 for 0