## 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 21

Page 396

That is, the terms "

interchangeably. ... We now define a best critical region (and hence a best

for

In this ...

That is, the terms "

**test**" and "critical region" can, in this sense, be usedinterchangeably. ... We now define a best critical region (and hence a best

**test**)for

**testing**the simple hypothesis**H0**against the alternative simple hypothesis HuIn this ...

Page 406

of size 0.05 for

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

affords an illustration of a

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**H0**against ...

Page 444

(a) Find a complete sufficient statistic for 9. (b) If a = p = ^, find the sequential

probability ratio test of H0:9 = 2 against : 9 = 3. 9.49. Let X have a Poisson p.d.f.

with parameter 9. We shall use a random sample of size n to

against H, ...

(a) Find a complete sufficient statistic for 9. (b) If a = p = ^, find the sequential

probability ratio test of H0:9 = 2 against : 9 = 3. 9.49. Let X have a Poisson p.d.f.

with parameter 9. We shall use a random sample of size n to

**test H0**: 9 = 1against H, ...

### 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