The Mathematical Theory of Probabilities and Its Application to Frequency Curves and Statistical Methods
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The Mathematical Theory of Probabilities and Its Application to Frequency Curves and Statistical Methods

The Mathematical Theory of Probabilities and Its Application to Frequency Curves and Statistical Methods


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 Excerpt: ...we notice that the mean error of the relative frequency numbers decreases as the number of observations increases. CHAPTER X. THE THEORY OF DISPERSION AND THE CRITERIA OF LEXIS AND CHARLIER. 73. Bernoullian, Poisson and Lexis Series.--In the previous chapter we limited our discussion to single sets consisting of s individual trials and found in the mean error and the criterion of Tchebycheff a measure for the uncertainty with which the relative frequency ratio ajs as well as the absolute frequency a were affected. How will matters now turn out if, instead of a single set, we make N sets of trials? As already mentioned in paragraph 54, in general in N such sets we shall obtain N different values of a, denoting the absolute frequency of the event represented by the sequence ai, a2, a3, ... aN. Our object is now to investigate whether the distribution of the above values of a around a certain norm is subject to some simple mathematical law and if possible to find a measure for such distributions. In this connection it is of great importance whether the postulated a priori probabilities remain constant or not during the N sample sets. Three cases are of special importance to us.1 1. The probability of the happening of the event remains constant during all the N sets. The series as given by the absolute frequencies in each set is known as a Bernoullian Series. 2. The same probability varies from trial to trial inside each of N sample sets, the variations being the same from set to set. The series as given by the absolute frequencies is in this case known as a Poisson Series. 3. The probability remains constant in any one particular set but varies from set to set. The absolute frequency series as produced in this way is called a Lexis Series. The above definition ..


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Product Details
  • ISBN-13: 9781152014046
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 82
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1152014048
  • Publisher Date: 08 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 163 gr

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