## 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. |

### From inside the book

Results 1-3 of 49

Page 283

probability of rejecting this true

research workers find it very undesirable to have such a high probability as 5

assigned to this kind of mistake: namely the rejection of H0 when H0 is a true

hypothesis.

probability of rejecting this true

**hypothesis H0**is \. Many statisticians andresearch workers find it very undesirable to have such a high probability as 5

assigned to this kind of mistake: namely the rejection of H0 when H0 is a true

hypothesis.

Page 406

of size 0.05 for testing the simple

hypothesis in the composite hypothesis Hx : 9 > 2. The preceding example

affords an illustration of a test of a simple

against ...

of size 0.05 for testing the simple

**hypothesis H0**:9 = 2 against each simplehypothesis in the composite hypothesis Hx : 9 > 2. The preceding example

affords an illustration of a test of a simple

**hypothesis H0**that is a best test of H0against ...

Page 506

The original hypothesis was then replaced by the less restrictive

r(XeA,) = pi0, i = 1, 2, . . . , k; and a chi-square test, based upon a statistic that was

denoted by Qk _ , , was used to test the

The original hypothesis was then replaced by the less restrictive

**hypothesis H0**:¥r(XeA,) = pi0, i = 1, 2, . . . , k; and a chi-square test, based upon a statistic that was

denoted by Qk _ , , was used to test the

**hypothesis H0**against all alternative ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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