Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 134
... distribution with α = 4 and ẞ = 3 . Remark . The gamma distribution is not only a good model for waiting times , but ... chi - square distribution , and any f ( x ) of this form is called a chi - square p.d.f. The mean and the variance ...
... distribution with α = 4 and ẞ = 3 . Remark . The gamma distribution is not only a good model for waiting times , but ... chi - square distribution , and any f ( x ) of this form is called a chi - square p.d.f. The mean and the variance ...
Page 485
... distribution with positive definite covariance matrix V ; here the necessary and sufficient condition that Q have a chi - square distribution is AVA = A. EXERCISES · - 10.35 . Let Q = X1X2 X3X4 , where X1 , X2 , X3 , X4 is a random ...
... distribution with positive definite covariance matrix V ; here the necessary and sufficient condition that Q have a chi - square distribution is AVA = A. EXERCISES · - 10.35 . Let Q = X1X2 X3X4 , where X1 , X2 , X3 , X4 is a random ...
Page 562
... distribution , 233 , 237 , 243 , 253 , 294 , 380 Limiting moment - generating function , 243 Linear discriminant ... chi - square estimates , 298 Minimum mean - square - error estimates , 310 Mode , 43 Model , 15 , 40 , 78 , 325 , 472 ...
... distribution , 233 , 237 , 243 , 253 , 294 , 380 Limiting moment - generating function , 243 Linear discriminant ... chi - square estimates , 298 Minimum mean - square - error estimates , 310 Mode , 43 Model , 15 , 40 , 78 , 325 , 472 ...
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A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²