This preview shows page 1. Sign up to view the full content.
Unformatted text preview: elihood function similarly but with the p.f. P (Y = y; ) replaced by the p.d.f. evaluated at the observed values. For independent observations Yi , i = 1, 2, ..., n from the same p.d.f. f (y ; ), the joint p.d.f. of (Y1 , Y2 , ..., Yn ),
i =1 f (yi ; ) is used for the likelihood function. n For n independent observations y1 , y2 , ..., yn from a continuous p.d.f. f (y ; ), we de...ne the likelihood function as L ( ) = L (; y) = f (yi ; )
i =1
Statistics and Actuarial Science () Model Fitting, Estimation and Checking n for 2 .
Jan 2013 23 / 45 Likelihood for an Exponential Population
Suppose Y = lifetime of a randomly selected light bulb in a large population and that Y Exponential( ), having p.d.f. f (y ; ) = 1 e for y > 0, where > 0.
y / A random sample of light bulbs is tested and the lifetimes y1 , . . . , yn are observed Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 24 / 45 Likelihood for an Exponential Population
Suppose Y = lifetime of a randomly selected light bulb in a large population and that Y Exponential( ), having p.d.f. f (y ; ) = 1 e for y > 0, where > 0.
y / A random sample of light bulbs is tested and the lifetimes y1 , . . . , yn are observed Likelihood function for is L( ) = n i =1 1 yi / e = 1 n exp i =1 yi / n for > 0. Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 24 / 45 Likelihood for an Exponential Population
Suppose Y = lifetime of a randomly selected light bulb in a large population and that Y Exponential( ), having p.d.f. f (y ; ) = 1 e for y > 0, where > 0.
y / A random sample of light bulbs is tested and the lifetimes y1 , . . . , yn are observed Likelihood function for is L( ) = n i =1 1 yi / e = 1 n exp
1 i =1 n yi / n for > 0. Loglikelihood `( ) = n log i =1 yi for > 0. Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 24 / 45 Likelihood for an Exponential Population
Suppose Y = lifetime of a randomly selected light bulb in a large pop...
View
Full
Document
This note was uploaded on 04/17/2013 for the course STAT 231 taught by Professor Cantremember during the Winter '08 term at Waterloo.
 Winter '08
 CANTREMEMBER
 Statistics

Click to edit the document details