Introduction to Mathematical StatisticsAn exceptionally clear and impeccably accurate presentation of statistical applications and more advanced theory. Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics. More modern technology is used in considering limiting distributions, making the presentations more clear and uniform. |
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Page 44
(b) fx) = 12^(1 — x), 0 < x < 1, zero elsewhere. (c) J(x) = (^)x2e~x, 0 < x < oo, zero
elsewhere. ' 3. 1.67. A median of a distribution of one random variable X of the
discrete or continuous type is a value of x such that Pr (X < x) < \ and Pr (X < x) > \.
(b) fx) = 12^(1 — x), 0 < x < 1, zero elsewhere. (c) J(x) = (^)x2e~x, 0 < x < oo, zero
elsewhere. ' 3. 1.67. A median of a distribution of one random variable X of the
discrete or continuous type is a value of x such that Pr (X < x) < \ and Pr (X < x) > \.
Page 45
for the discrete type of random variable, and for the continuous type of random
variable. We speak of a distribution function F(x) as being of the continuous or
discrete type, depending on whether the random variable is of the continuous or
...
for the discrete type of random variable, and for the continuous type of random
variable. We speak of a distribution function F(x) as being of the continuous or
discrete type, depending on whether the random variable is of the continuous or
...
Page 47
and 1.8, and the fact that the probability set function P is countably additive; that
is, P enjoys (b) of Definition 7. The preceding discussion may be summarized in
the following manner: A distribution function F(x) is a nondecreasing function of x,
...
and 1.8, and the fact that the probability set function P is countably additive; that
is, P enjoys (b) of Definition 7. The preceding discussion may be summarized in
the following manner: A distribution function F(x) is a nondecreasing function of x,
...
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Common terms and phrases
Accordingly approximate best critical region chi-square distribution complete sufficient statistic conditional p.d.f. conditional probability confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random depend upon 9 discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters equation estimator of 9 Example Exercise F-distribution gamma distribution given H0 is true independent random variables integral joint p.d.f. Let the random Let Xu X2 likelihood function limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Yx percent confidence interval Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random sample random variables Xx reject H0 respectively sample space Section Show significance level statistic for 9 subset testing H0 theorem u(Xu X2 unbiased estimator XuX2 Xx and X2 Yu Y2 zero elsewhere
Bibliographic information
| Title | Introduction to Mathematical Statistics Prentice Hall International Editions |
| Author | Robert V. Hogg |
| Contributor | Allen Thornton Craig |
| Edition | 5, illustrated |
| Publisher | Prentice Hall, 1995 |
| Original from | the University of Michigan |
| Digitized | 27 Jan 2010 |
| ISBN | 0023557222, 9780023557224 |
| Length | 564 pages |
| Export Citation | BiBTeX EndNote RefMan |