Introduction to Mathematical Statistics |
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Page 118
... Likelihood Estimation of Parameters . In this section we present a brief discussion of a very general method of point estimation of parameters known as the method of maximum likelihood . Consider a random sample X1 , X2 , ... , Xn from ...
... Likelihood Estimation of Parameters . In this section we present a brief discussion of a very general method of point estimation of parameters known as the method of maximum likelihood . Consider a random sample X1 , X2 , ... , Xn from ...
Page 121
... likelihood statistic Ô is a function of the sufficient statistic Y1 = u1 ( X1 , X2 , ... , Xn ) . This important fact was illustrated in Ex- amples 1 , 2 ... likelihood statistic ê for $ 5.10 ] MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS 121.
... likelihood statistic Ô is a function of the sufficient statistic Y1 = u1 ( X1 , X2 , ... , Xn ) . This important fact was illustrated in Ex- amples 1 , 2 ... likelihood statistic ê for $ 5.10 ] MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS 121.
Page 189
... likelihood ratio principle leads to the same test , when testing a null simple hypothesis Ho against an alternative simple hypothesis H1 , as that given by the Neyman - Pearson theorem . Note that there are only two points in 2 . n 9.24 ...
... likelihood ratio principle leads to the same test , when testing a null simple hypothesis Ho against an alternative simple hypothesis H1 , as that given by the Neyman - Pearson theorem . Note that there are only two points in 2 . n 9.24 ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²