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 134
... gamma distribution with α = 4 and ẞ = 3 . Remark . The gamma distribution is not only a good model for waiting times , but one for many nonnegative random variables of the continuous type . For illustration , the distribution of certain ...
... gamma distribution with α = 4 and ẞ = 3 . Remark . The gamma distribution is not only a good model for waiting times , but one for many nonnegative random variables of the continuous type . For illustration , the distribution of certain ...
Page 137
... distribution functions of the gamma and Poisson distributions . Hint : Either integrate by parts k - 1 times or simply note that the " antiderivative " of ... distribution with p.d.f. Sec . 3.3 ] The Gamma and Chi - Square Distributions 137.
... distribution functions of the gamma and Poisson distributions . Hint : Either integrate by parts k - 1 times or simply note that the " antiderivative " of ... distribution with p.d.f. Sec . 3.3 ] The Gamma and Chi - Square Distributions 137.
Page 372
... gamma distribution with parameters α = r / 2 and B = 2 / r , where r is a positive integer . Show that X has a marginal t - distribution with r degrees of freedom . This procedure is called compounding , and it may be used by a Bayesian ...
... gamma distribution with parameters α = r / 2 and B = 2 / r , where r is a positive integer . Show that X has a marginal t - distribution with r degrees of freedom . This procedure is called compounding , and it may be used by a Bayesian ...
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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 Find the p.d.f. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²