Download e-book for iPad: Computing in Accelerator Design and Operation by W. Busse, R. Zelazny

By W. Busse, R. Zelazny

ISBN-10: 3540139095

ISBN-13: 9783540139096

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2 First Exploratory Data Analysis Tools 15 Fig. 8. Examples of histograms: PCS index (left) and S&P weekly log-returns (right). index) > hist(WSPLRet) > par(mfrow=c(1,1)) The first command is intended to divide the plotting area into a 1 × 2 matrix in which plots are inserted in sequence. The next two commands actually produce the histograms. index and WSPLRet whose creation was explained earlier. Histograms are produced in S-Plus with the command hist. See the help file for details on the options available, including the choice of the number of bins, their size, .

Xn . d. random variables X1 , X2 , . . , Xn with common cdf F , and the statistical challenge is to estimate F and/or some of its characteristics from the data. Mean and standard deviation of the distribution are typical examples of characteristics targeted for estimation. However, in financial applications, V aRq , ESq , Θq , . . are also often of crucial importance. Because all of the quantities we want to estimate are functions of the cdf F , the general strategy is to use the sample observations to derive an estimate, say Fˆ , of the cdf F , and then to use the characteristics of Fˆ as estimates of the corresponding characteristics of F .

A little song and dance is needed to make the argument mathematically sound in the general case, but we shall not worry about such details here. So we proved that: FX cdf of X =⇒ U = FX (X) ∼ U (0, 1). 25) This simple mathematical statement has a far-reaching converse. 24) from right to left we get: 32 1 UNIVARIATE EXPLORATORY DATA ANALYSIS Fact 2 If U ∼ U (0, 1) and F is a cdf, then if we define the random variable X by X = F −1 (U ) we necessarily have FX = F . Indeed: P{X ≤ x} = P{F −1 (U ) ≤ x} = P{U ≤ F (x)} = F (x).

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Computing in Accelerator Design and Operation by W. Busse, R. Zelazny


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