Introduction to Mathematical Statistics |
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Page 318
... Noncentral x2 and Noncentral F n Let X1 , X2 , ... , X , denote mutually stochastically independent random variables that are n ( p , o2 ) , i = 1 , 2 , ... , n and let Y = n Σ X2 / o2 . If each μ , is zero ... Noncentral x2 and Noncentral F.
... Noncentral x2 and Noncentral F n Let X1 , X2 , ... , X , denote mutually stochastically independent random variables that are n ( p , o2 ) , i = 1 , 2 , ... , n and let Y = n Σ X2 / o2 . If each μ , is zero ... Noncentral x2 and Noncentral F.
Page 319
... noncentral chi - square distribution which has the parameters ⁄ and 0 ; and we shall say that a random variable is x2 ( r , 0 ) to mean that the random variable has this kind of distribution . The ... Noncentral x2 and Noncentral F 319.
... noncentral chi - square distribution which has the parameters ⁄ and 0 ; and we shall say that a random variable is x2 ( r , 0 ) to mean that the random variable has this kind of distribution . The ... Noncentral x2 and Noncentral F 319.
Page 381
... Noncentral chi - square , see Distribu- tion Noncentral F , see Distribution Noncentral parameter , 292 , 319 , 320 Noncentral T , see Distribution Nonparametric , 294 Normal distribution , see Distribution Order statistics , 168 ...
... Noncentral chi - square , see Distribu- tion Noncentral F , see Distribution Noncentral parameter , 292 , 319 , 320 Noncentral T , see Distribution Nonparametric , 294 Normal distribution , see Distribution Order statistics , 168 ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES F distribution function F(x given hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variables X₁ variance o² W₁ X₁ X₁ and X2 X₂ x²(n Y₂ Z₁ zero elsewhere μ₁ σ²