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. |
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Page 134
... distribution with a = 4 and ß = 3 . Remark . The gamma distribution is not only a good model for waiting times , but ... chi - square distribution , and any f ( x ) of this form is called a chi - square p.d.f. The mean and the variance ...
... distribution with a = 4 and ß = 3 . Remark . The gamma distribution is not only a good model for waiting times , but ... chi - square distribution , and any f ( x ) of this form is called a chi - square p.d.f. The mean and the variance ...
Page 484
... chi - square distribution . Assume that X'AX / σ2 is x2 ( k ) . Then M ( t ) = [ ( 1 − 2ta1 ) ( 1 − 2ta2 ) · · · ( 1 − 2ta , ) ] − 1 / 2 = ( 1 − 2t ) −k / 2 , - or , equivalently , - • 2ta , ) ( 1 - 2ta2 )・・・( 1 − 2ta ...
... chi - square distribution . Assume that X'AX / σ2 is x2 ( k ) . Then M ( t ) = [ ( 1 − 2ta1 ) ( 1 − 2ta2 ) · · · ( 1 − 2ta , ) ] − 1 / 2 = ( 1 − 2t ) −k / 2 , - or , equivalently , - • 2ta , ) ( 1 - 2ta2 )・・・( 1 − 2ta ...
Page 562
... distribution , 233 , 237 , 243 , 253 , 294 , 380 Limiting moment - generating function , 243 Linear discriminant ... chi - square estimates , 298 Minimum mean - square - error estimates , 310 Mode , 43 Model , 15 , 40 , 78 , 325 , 472 ...
... distribution , 233 , 237 , 243 , 253 , 294 , 380 Limiting moment - generating function , 243 Linear discriminant ... chi - square estimates , 298 Minimum mean - square - error estimates , 310 Mode , 43 Model , 15 , 40 , 78 , 325 , 472 ...
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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 Find the p.d.f. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics 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 subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²