Introduction to Mathematical Statistics
An 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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Some Special Distributions
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accept Accordingly alternative approximate associated assume called chips complete sufficient statistic compute confidence interval Consider constant continuous type converges critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function distribution with mean equal equation equivalent estimator event Example Exercise exists expectation experiment fact Find gamma given Hence hypothesis H illustration independent inequality integral joint p.d.f. known Let X1 likelihood limiting marginal matrix maximum mean Moreover normal distribution observations obtain order statistics parameters percent Poisson distribution positive probability density functions problem prove random sample random variable ratio reject Remark represent respectively result selected Show significance level simple sufficient statistic Suppose theorem transformation true unbiased estimator unknown variance write zero elsewhere