Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 41
Page 86
... order statistics Y1 = minimum Yı of X1 , X2 , X3 ; Y2 = middle in magnitude of X1 , X2 , X3 ; Y3 = maximum of X1 , X2 , X3 is g ( Y1 , Y2 , Y3 ) = = | J1 \ f ( Y1 ) f ( Y2 ) f ( Y3 ) + | J2 \ f ( Y2 ) f ( Y1 ) f ( Y3 ) + ··· + | J6 | f ...
... order statistics Y1 = minimum Yı of X1 , X2 , X3 ; Y2 = middle in magnitude of X1 , X2 , X3 ; Y3 = maximum of X1 , X2 , X3 is g ( Y1 , Y2 , Y3 ) = = | J1 \ f ( Y1 ) f ( Y2 ) f ( Y3 ) + | J2 \ f ( Y2 ) f ( Y1 ) f ( Y3 ) + ··· + | J6 | f ...
Page 88
... Order Statistics . Certain functions of the order statistics Y1 , Y2 , ... , Y , are important statistics themselves . A few of these are ( a ) Y , Y1 , which is called the range of the random sample ; ( b ) ( Y1 + Y ) / 2 , which is ...
... Order Statistics . Certain functions of the order statistics Y1 , Y2 , ... , Y , are important statistics themselves . A few of these are ( a ) Y , Y1 , which is called the range of the random sample ; ( b ) ( Y1 + Y ) / 2 , which is ...
Page 162
... order statistics of a random sample of size 4 from a distribution of the continuous type . The probability that the random interval ( Y1 , Y4 ) includes the median 0.5 of the distribution will be computed . We have Pr ( Y1 < 0.5 < Y1 ) ...
... order statistics of a random sample of size 4 from a distribution of the continuous type . The probability that the random interval ( Y1 , Y4 ) includes the median 0.5 of the distribution will be computed . We have Pr ( Y1 < 0.5 < Y1 ) ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
14 other sections not shown
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