Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
From inside the book
Results 1-3 of 7
Page 325
... depend upon 0 , the factorization theorem implies that Z = u ( Y1 ) is also ... 9 for each y1 , is exactly the same as { ( X1 , X2 , . . . , Xn ) : v ( X1 ... depend upon the fact that a certain model is true . For illustration , knowing ...
... depend upon 0 , the factorization theorem implies that Z = u ( Y1 ) is also ... 9 for each y1 , is exactly the same as { ( X1 , X2 , . . . , Xn ) : v ( X1 ... depend upon the fact that a certain model is true . For illustration , knowing ...
Page 341
... depend upon a single parameter 0 , but perhaps upon two ( or more ) ... 9 n Definition 4. Let X1 , X2 , . X , denote a random sample from a ... depend upon 0 , or 02 . As may be anticipated , the factorization theorem can be extended . In ...
... depend upon a single parameter 0 , but perhaps upon two ( or more ) ... 9 n Definition 4. Let X1 , X2 , . X , denote a random sample from a ... depend upon 0 , or 02 . As may be anticipated , the factorization theorem can be extended . In ...
Page 409
... depend upon 0. Consequently , the where k2 ( X1 , X2 ,. ratio L ( 0 ' ; X1 ... depends upon x1 , x2 , . . . , x , only through u ( x1 , x2 , . . . , x ... 9 is an increasing function of y = u ( x1 , x2 , . . . , x ) . In such a ...
... depend upon 0. Consequently , the where k2 ( X1 , X2 ,. ratio L ( 0 ' ; X1 ... depends upon x1 , x2 , . . . , x , only through u ( x1 , x2 , . . . , x ... 9 is an increasing function of y = u ( x1 , x2 , . . . , x ) . In such a ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²