Distribution Table

# Distribution Table - Special Discrete Distributions...

This preview shows pages 1–5. Sign up to view the full content.

Special Discrete Distributions Notation and Parameters p.f. Mean Variance m.g.f. Binomial X ! BIN ! n , p " n x !" p x q n " x np npq ! pe t ! q " n 0 " p " 1 x # 0,1,. .., n q # 1 " p Bernoulli X ! Bernoulli ! p " p x q 1 " x p pq pe t ! q 0 " p " 1 x # 0,1 q # 1 " p Negative Binomial X ! NB ! k , p " " k x p k ! " q " x kq p kq p 2 ! p 1 " qe t " k 0 " p " 1 q # 1 " px # .. t " " log q Geometric X ! GEO ! p " pq x q / pq / p 2 p 1 " qe t 0 " p " 1 x # t " " log q q # 1 " p

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Special Discrete Distributions Notation and Parameters p.f. Mean Variance m.g.f. Hypergeometric X ! HYP ! n , M , N " M x !" N " M n " x / N n nM / Nn M N ! 1 " M N " N " n N " 1 * n # 1,2, # , Nx # 0,1, # , n M # # , N Poisson X ! POI ! ! " e " ! ! x / x ! !! e ! ! e t " 1 " ! \$ 0 x # # Discrete Uniform X ! DU ! N " 1/ N N ! 1 2 N 2 " 1 12 1 N e t " e ! N ! 1 " t 1 " e t N # # x # # , Nt # 0 * Not Tractable
Special Continuous Distributions Notation and Parameters p.d.f. Mean Variance m.g.f. Uniform X ! UNIF ! a , b " 1/ ! b " a " a ! b 2 ! b " a " 2 12 e bt " e at ! b " a " t a " ba \$ x \$ bt # 0 Normal X ! N ! ! , " 2 " 1 2 # " e " \$! x " ! " / " % 2 /2 !" 2 e ! t ! " 2 t 2 /2 " 2 \$ 0 Gamma X ! GAM ! \$ , % " 1 % \$ % ! \$ " x \$ " 1 e " x / % \$% \$% 2 ! 1 " % t " " \$ % \$ 0 x \$ 0 \$ \$ 0 t " 1/ % Inverted Gamma X ! IG ! \$ , % " 1 % \$ % ! \$ " x " \$ " 1 e " 1/ ! % x " 1 % ! \$ " 1 " 1 % 2 ! \$ " 1 " 2 ! \$ " 2 " * % \$ 0 \$ \$ 0 x \$ 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Special Continuous Distributions Notation and Parameters p.d.f. Mean Variance m.g.f.
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/21/2010 for the course MATHEMATIC stats taught by Professor Various during the Spring '10 term at Waterloo.

### Page1 / 7

Distribution Table - Special Discrete Distributions...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online