Mathematical Statistics and Data Analysis, Page 3
This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings.
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Distributions Derived from the Normal Distribution
Estimation of Parameters and Fitting of Probability Distributions
ˆθ ˆλ approximate assumption average Bayesian bootstrap boxplots calculate cell central limit theorem Chapter chi-square CN CN CN coefficient confidence interval correlation counts covariance degrees of freedom denote density function equal example expected Figure following table frequency function gamma distribution given histogram independent random variables joint density large number least squares Let X1 linear matrix maximum likelihood estimate measurements median method of moments moment-generating function normal density normal distribution null distribution null hypothesis observations p-value Poisson distribution population mean prior probability distribution probability plot problem Q-Q plot quantiles regression residuals sample mean sampling distribution Section Show significance level simple random sample standard deviation standard error standard normal Suppose test statistic total number unbiased uniform values Var(X versus zero