## Introduction to Mathematical StatisticsAn exceptionally clear and impeccably accurate presentation of statistical applications and more advanced theory. Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics. More modern technology is used in considering limiting distributions, making the presentations more clear and uniform. |

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Page 397

Robert V. Hogg. We shall use one random value of X to test the simple

hypothesis H0:9 = \ against the alternative simple hypothesis //, : 9 = f, and we

shall first assign the significance level of the test to be a = ^. We seek a

Robert V. Hogg. We shall use one random value of X to test the simple

hypothesis H0:9 = \ against the alternative simple hypothesis //, : 9 = f, and we

shall first assign the significance level of the test to be a = ^. We seek a

**best****critical region**of ...Page 406

The preceding example affords an illustration of a test of a simple hypothesis H0

that is a

composite hypothesis Hx . We now define a

is a

The preceding example affords an illustration of a test of a simple hypothesis H0

that is a

**best**test of H0 against every simple hypothesis in the alternativecomposite hypothesis Hx . We now define a

**critical region**, when it exists, whichis a

**best**...Page 408

The first of these two expressions defines a

' against the hypothesis 9 = 9" provided that 9" > 9', while the second expression

defines a

The first of these two expressions defines a

**best critical region**for testing H0:9 = 9' against the hypothesis 9 = 9" provided that 9" > 9', while the second expression

defines a

**best critical region**for testing H0:9 = 9' against the hypothesis 9 = 9" ...### What people are saying - Write a review

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### Common terms and phrases

Accordingly approximate best critical region chi-square distribution complete sufficient statistic conditional p.d.f. conditional probability confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random depend upon 9 discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters equation estimator of 9 Example Exercise F-distribution gamma distribution given H0 is true hypothesis H0 independent random variables integral joint p.d.f. Let the random Let Xu X2 limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Xu percent confidence interval Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random sample random variables Xx reject H0 respectively sample space Section Show significance level simple hypothesis statistic for 9 sufficient statistic testing H0 theorem unbiased estimator variance a2 Xx and X2 Yu Y2 zero elsewhere