Introduction to Mathematical Statistics |
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Page 190
Robert V. Hogg, Allen Thornton Craig. CHAPTER TEN CERTAIN QUADRATIC FORMS A homogeneous polynomial of degree two in n variables is called a quadratic form in those variables . If both the variables and the coeffi- cients are real , the form ...
Robert V. Hogg, Allen Thornton Craig. CHAPTER TEN CERTAIN QUADRATIC FORMS A homogeneous polynomial of degree two in n variables is called a quadratic form in those variables . If both the variables and the coeffi- cients are real , the form ...
Page 191
... quadratic forms will be needed to carry out the test in an expeditious manner . In Section 10.1 we shall make a ... form in the variables X1 μ . Indeed , as pointed out in the introductory remarks to this chapter , nS2 is also a quadratic ...
... quadratic forms will be needed to carry out the test in an expeditious manner . In Section 10.1 we shall make a ... form in the variables X1 μ . Indeed , as pointed out in the introductory remarks to this chapter , nS2 is also a quadratic ...
Page 198
... quadratic form ab S2 , which is a total sum of squares , is resolved into several component parts . In this section another problem in the analysis of variance will be investigated . Let Xij , i = 1 , 2 , ... , a and j = 1 , 2 , ... , b ...
... quadratic form ab S2 , which is a total sum of squares , is resolved into several component parts . In this section another problem in the analysis of variance will be investigated . Let Xij , i = 1 , 2 , ... , a and j = 1 , 2 , ... , b ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²