By Anders Hald
This ebook deals an in depth background of parametric statistical inference. overlaying the interval among James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference via inverse chance; the relevant restrict theorem and linear minimal variance estimation through Laplace and Gauss; errors concept, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. full of life biographical sketches of a number of the major characters are featured all through, together with Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. additionally tested are the jobs performed by way of DeMoivre, James Bernoulli, and Lagrange.
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Additional info for A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 (Sources and Studies in the History of Mathematics and Physical Sciences)
He seems to have led a quiet life, mainly occupied with his scholarly interests, beginning with theology, moving to mathematics and the natural sciences, and ending with statistical inference. He was elected a Fellow of the Royal Society in 1742. When Bayes died in 1761 his relatives asked Richard Price (1723—1791), another Presbyterian minister, to examine the mathematical papers left by Bayes. Price found a paper on Stirling’s formula and the paper “An Essay Towards Solving a Problem in the Doctrine of Chances,” which he got published in two parts in the Phil.
A fifth volume was published in 1825 . After having completed his astronomical work in 1805, he resumed work on probability and statistics and published the Théorie Analytique des Probabilités (TAP), , the most inﬂuential book on probability and statistics ever written. In  he added the Essai Philosophique sur les Probabilités as a popular introduction to the second edition of the TAP. The Essay was also published separately and he kept on revising and enlarging it until the sixth edition.
Thomas Simpson (1710—1761), , had derived the sampling distribution of the mean for observations from a symmetric triangular distribution, a rather complicated function, and had shown numerically that P (|x| < k) > P (|x1 | < k) for 42 5 Laplace’s Theory of Inverse Probability n = 6 and two values of k, from which he concluded that it is advantageous to use the mean as the estimate of . As a first step Laplace  introduces a new error distribution with infinite support, the double exponential distribution f (x|, m) = m m|x| e , 4 < x < 4, 4 < < 4, 0 < m < 4.