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In this classic of statistical mathematical theory, Harald Cramér joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. The result of Cramér's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow. For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance.

Mathematical statistics --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistique mathématique --- Mathematical statistics. --- Statistique mathématique --- Statistique mathématique. --- Distribution (théorie des probabilités) --- Distribution (Probability theory) --- A priori probability. --- Addition theorem. --- Additive function. --- Analysis of covariance. --- Arithmetic mean. --- Axiom. --- Bayes' theorem. --- Bias of an estimator. --- Binomial distribution. --- Binomial theorem. --- Bolzano–Weierstrass theorem. --- Borel set. --- Bounded set (topological vector space). --- Calculation. --- Cartesian product. --- Central moment. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Coefficient. --- Commutative property. --- Confidence interval. --- Convergence of random variables. --- Correlation coefficient. --- Degeneracy (mathematics). --- Degrees of freedom (statistics). --- Diagram (category theory). --- Dimension. --- Distribution (mathematics). --- Distribution function. --- Empirical distribution function. --- Equation. --- Estimation theory. --- Estimation. --- Identity matrix. --- Independence (probability theory). --- Interval (mathematics). --- Inverse probability. --- Invertible matrix. --- Joint probability distribution. --- Laplace distribution. --- Lebesgue integration. --- Lebesgue measure. --- Lebesgue–Stieltjes integration. --- Likelihood function. --- Limit (mathematics). --- Linear regression. --- Logarithm. --- Logarithmic derivative. --- Logarithmic scale. --- Marginal distribution. --- Mathematical analysis. --- Mathematical induction. --- Mathematical theory. --- Mathematics. --- Matrix (mathematics). --- Maxima and minima. --- Measure (mathematics). --- Method of moments (statistics). --- Metric space. --- Minor (linear algebra). --- Moment (mathematics). --- Moment matrix. --- Normal distribution. --- Numerical analysis. --- Parameter. --- Parity (mathematics). --- Poisson distribution. --- Probability distribution. --- Probability theory. --- Probability. --- Proportionality (mathematics). --- Quantity. --- Random variable. --- Realization (probability). --- Riemann integral. --- Sample space. --- Sampling (statistics). --- Scientific notation. --- Series (mathematics). --- Set (mathematics). --- Set function. --- Sign (mathematics). --- Standard deviation. --- Statistic. --- Statistical Science. --- Statistical hypothesis testing. --- Statistical inference. --- Statistical regularity. --- Statistical theory. --- Subset. --- Summation. --- Theorem. --- Theory. --- Transfinite number. --- Uniform distribution (discrete). --- Variable (mathematics). --- Variance. --- Weighted arithmetic mean. --- Z-test. --- Distribution (théorie des probabilités)