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 262
... likelihood estimator of 0. The observed value of Ô , n namely Σx¡ / n , is called the maximum likelihood estimate of ... function of 0. When so regarded , it is called the likelihood function L of the random sample , and we write n L ( 0 ...
... likelihood estimator of 0. The observed value of Ô , n namely Σx¡ / n , is called the maximum likelihood estimate of ... function of 0. When so regarded , it is called the likelihood function L of the random sample , and we write n L ( 0 ...
Page 264
... likelihood estimators are consistent . The preceding definitions and properties are easily generalized . Let X , Y ... function of ( 01 , 02 , . . . , 0m ) E 2 , is called the likelihood function of the random variables . Then those ...
... likelihood estimators are consistent . The preceding definitions and properties are easily generalized . Let X , Y ... function of ( 01 , 02 , . . . , 0m ) E 2 , is called the likelihood function of the random variables . Then those ...
Page 561
... likelihood , 262 , 324 , 380 , 385 , 389 minimum chi - square , 298 minimum mean - square - error , 310 unbiased ... function , 441 Frequency , 2 relative , 2 , 12 , 17 Function , characteristic , 64 decision , 308 , 433 distribution ...
... likelihood , 262 , 324 , 380 , 385 , 389 minimum chi - square , 298 minimum mean - square - error , 310 unbiased ... function , 441 Frequency , 2 relative , 2 , 12 , 17 Function , characteristic , 64 decision , 308 , 433 distribution ...
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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 g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²