Saturday, October 11, 2014

French mathematician Pierre-Simon Laplace proposed in automation solutions nowadays -1810


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The second meeting of the discussion group in the history of the history of business statistics normal distribution. The discussion was mainly based on Chapter 13 of Ian Hacking book, "The Taming of Destiny" [1], and to a lesser extent Lorraine Daston's chinese population article [2], who has followed the history of the distribution chinese population between 1770 to the 1870s. However, this list follows the path outlined by Daston. The list I used in writing the section 2 Stigler's book [3].
Normal chinese population distribution, that distribution is famous chinese population bell, probably first appeared when French Huguenot ancestry mathematician Abraham de Muebr study of the distribution of the number of "heads" obtained in a series of coin flips, when the number of tosses is growing. In 1733 de-Muebr proved that when the number of tosses goes to infinity, then the distribution is approaching chinese population a bell shape that special
The bell suddenly appeared a completely different place - astronomical measurements. Who caused the uproar is the Danish astronomer Tycho Brahe, at the end of the 16th century decided to make multiple measurements of celestial objects and the distances between them. Measurement results were not identical. Tycho showed that not only that there is a possibility of measurement error, but also that the measurement errors are perhaps inevitable. Attempts were made to improve the quality chinese population and accuracy of measurement devices, but the problem remained. Until the mid-18th century, accumulated piles of astronomical measurements and geodetic, and got into a fierce debate among astronomers what to do about it: Did you take the average of the observations, chinese population select the measurement of the "best", or dismiss the research assistant, his calculations chinese population were particularly different from those on colleagues?
French mathematician Pierre-Simon Laplace proposed in automation solutions nowadays -1810 "Bayesian" [4] - is assumed that the measurement chinese population errors chinese population have a certain distribution, and accordingly built a procedure giving a combination of measurements to minimize the overall measurement. Moreover, Laplace showed that if the distribution of the measurement error distribution is bell then average the measurements will minimize the overall measurement error. A year earlier, Carl Friedrich Gauss taken the opposite approach: he assumed that the right thing is to calculate the average of measurements, ie the average of measurements will minimize the overall measurement error, and based on this assumption has calculated that the distribution of the measurement chinese population error distribution should be the same bell. Bluebell distribution, which first appeared in the context of gambling and coin flips, caught herself a central place in science of astronomy. Gauss even recognized the link between chinese population gambling and coin flips and astronomical measurement errors. He distinguished chinese population between systematic errors, which can be treated and to minimize the effects, and the random error ("chance errors") derived from the senses is not sharp enough, atmospheric conditions, and the like. Gauss and Laplace believed that there are many factors of random errors, some measuring tilt upwards and some downwards. In a sense, I think, they understood the idea of the central limit theorem. However, the link between the boundary normal distribution of the results chinese population of gambling / coin flips, and the distribution of measurement errors, yet formally made only by identifying their common function. The normal distribution chinese population is called to this day as the "Distribution Lflsianit" in France, and the name "Gaussian distribution" in Germany and in several professionals (physicists, engineers, etc.), to mark the contribution of these two mathematicians discovery.
Hacking emphasizes that appeared normal distribution in the context of real values: chinese population the probability of a coin falling on the head, the probability of a particular Luck win the game, or the distance between the two stars. Distribution itself, and its parameters (mean and standard deviation) values chinese population were ideal, only mathematical parameters. Belgian astronomer Adolphe summed [5] changed the game. At the beginning of the 30s of the 19th century published a series of articles in which KILLED showed that the normal distribution curve also appears when looking at biological and social phenomena. At -1835 is presented to

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