## A history of mathematical statistics from 1750 to 1930The long-awaited second volume of Anders Hald's history of the development of mathematical statistics. Anders Hald's A History of Probability and Statistics and Their Applications before 1750 is already considered a classic by many mathematicians and historians. This new volume picks up where its predecessor left off, describing the contemporaneous development and interaction of four topics: direct probability theory and sampling distributions; inverse probability by Bayes and Laplace; the method of least squares and the central limit theorem; and selected topics in estimation theory after 1830. In this rich and detailed work, Hald carefully traces the history of parametric statistical inference, the development of the corresponding mathematical methods, and some typical applications. Not surprisingly, the ideas, concepts, methods, and results of Laplace, Gauss, and Fisher dominate his account. In particular, Hald analyzes the work and interactions of Laplace and Gauss and describes their contributions to modern theory. Hald also offers a great deal of new material on the history of the period and enhances our understanding of both the controversies and continuities that developed between the different schools. To enable readers to compare the contributions of various historical figures, Professor Hald has rewritten the original papers in a uniform modern terminology and notation, while leaving the ideas unchanged. Statisticians, probabilists, actuaries, mathematicians, historians of science, and advanced students will find absorbing reading in the author's insightful description of important problems and how they gradually moved toward solution. |

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### Contents

Plan of the Book | 1 |

Some Results and Tools in Probability Theory | 11 |

The Distribution of the Arithmetic Mean 17561781 | 33 |

Copyright | |

28 other sections not shown

### Common terms and phrases

analysis approximation arithmetic mean assumes asymptotically normal Bayes Bayes's Bernoulli beta distribution Bienayme binomial distribution calculated Cauchy central limit theorem characteristic function Chebyshev considered corresponding curve denote density derives discussion E. S. Pearson Edgeworth equals error distribution estimation theory evaluation event example expansion finite Fisher follows formula Galton Gauss given gives Helmert Hence hypothesis independent interval introduces inverse probability Lagrange Laplace's large number large-sample leads least squares linear function location parameter mathematical median method of least minimizing Moivre normal distribution normal equations normal with mean notation notes number of observations obtained orthogonal paper Pearson points Poisson polynomials population posterior distribution principle prior probability theory problem proof proved Quetelet random variable ratio regression relative frequency remarks residuals result Setting solution solving standard deviation statistical Stigler sum of squares symmetric Thiele transformation true value uniformly distributed unknown variance writes zero