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. |
From inside the book
Results 1-3 of 60
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 295
... distribution function of a random variable that is x2 ( 1 ) . This is the ... chi - square distribution with 1 degree of freedom , we say , when n is a positive integer , that Q , has an approximate chi - square ... Chi - Square Tests 295.
... distribution function of a random variable that is x2 ( 1 ) . This is the ... chi - square distribution with 1 degree of freedom , we say , when n is a positive integer , that Q , has an approximate chi - square ... Chi - Square Tests 295.
Page 450
... distribution , and , accordingly , b - - Σ ( X1 , — á , . ) 2σ2 has a chi - square distribution with b – 1 degrees of freedom . – j = 1 Because the X , are independent , Q1 / 02 is the sum of a independent random variables , each ...
... distribution , and , accordingly , b - - Σ ( X1 , — á , . ) 2σ2 has a chi - square distribution with b – 1 degrees of freedom . – j = 1 Because the X , are independent , Q1 / 02 is the sum of a independent random variables , each ...
Other editions - View all
Common terms and phrases
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