Introduction to Mathematical Statistics |
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Page 88
... tion of the discrete type . All formulas in the text were derived under the assump- tion that the random sample is from a distribution of the continuous type and are not applicable . Why ? 4.7 . Functions of Order Statistics . Certain ...
... tion of the discrete type . All formulas in the text were derived under the assump- tion that the random sample is from a distribution of the continuous type and are not applicable . Why ? 4.7 . Functions of Order Statistics . Certain ...
Page 143
... tion may be used in problems of limiting distributions . A proof of the theorem requires a knowledge of that same facet of analysis that permitted us to assert that a moment - generating function , when it exists , uniquely determines a ...
... tion may be used in problems of limiting distributions . A proof of the theorem requires a knowledge of that same facet of analysis that permitted us to assert that a moment - generating function , when it exists , uniquely determines a ...
Page 144
... tion . On the other hand , the binomial distribution has two parameters , and tables for this distribution are very ungainly . To illustrate the use of the approximation , let Y have a binomial distribution with n = 50 and p 1/25 . Then ...
... tion . On the other hand , the binomial distribution has two parameters , and tables for this distribution are very ungainly . To illustrate the use of the approximation , let Y have a binomial distribution with n = 50 and p 1/25 . Then ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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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