Variate standard normal

To determine R(/) for the normal distribution, a standard normal variate must be calculated by the following formula ... 

Using the SND theory from Appendix I, the probability of failure, P, ean be determined from the Standard Normal variate, z, by ... 

We already know SM = 2.34 because it is the positive value of the Standard Normal variate, z, calculated above. The probability of failure per application of load... 

The area under the eurve to the left of i, — /i, = 0 relates to the probability of negative elearanee. This area ean be found from the SND table (Table 1, Appendix I) by determining the Standard Normal variate, z, where ... 

Comparing answers with that derived from the coupling equation, the Standard Normal variate is ... 

Standard deviation multiplier, Standard Normal variate Function of... 

An effective preprocessing method is the use of standard normal variates (SNV). This type of standardization boils down to considering each spectmm x, as a set of q observations and calculating their z-scores ... 

Standard normal variate (SNV) transformation is closely related to MSC (Barnes et al. 1989, 1993 Helland et al. 1995). SNV treats each spectmm separately by autoscaling the absorbance values (row-wise) by... 

Barnes, R. J., Dhanoa, M. S., Lister, S. J. Appl. Spectrosc. 43,1989, 772-777. Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Barnes, R. J., Dhanoa, M. S., Lister, S. J. J. Near Infrared Spectrosc. 1, 1993, 185-186. Correction of the description of standard normal variate (SNV) and De-Trend transformations in practical spectroscopy with applications in food and beverage analysis. Brereton, R. G. Chemometrics—Data Analysis for the Laboratory and Chemical Plant. Wiley, Chichester, United Kingdom, 2006. 

Fig. 9.1. The NIR spectra from strained and freeze-dried whole rumen liquor from sheep fed on ryegrass (solid line), and the bacterial (dotted line) and protozoal (dashed line) fractions. The standard normal variate and detrended data (SNV-DT) Is plotted vs. wavelength. Log 1/R = - log (Reflectance) and Is equivalent to absorbance.

Standard normal variate transformation and detrending of near infrared diffuse reflectance spectra. Applied Spectroscopy 43, 112-111. 

Barnes, R.)., Dhanoa, M. S., and Lister, S.). (1989). Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Appl. Spectrosc. 43(5), 772-777. 

Kohler, A., Zimonja, M., Segtnan, V., and Martens, H. (2009). Standard normal variate, multiplicative signal correction and extended multiplicative signal correction preprocessing in biospectroscopy. In "Comprehensive Chemometrics", (S. D. Brown, R. Tauler, and B. Walczak, Eds), Vol. 2, pp. 139-162. Elsevier, Amsterdam. 

The probability that the variable x takes a value between a and b is given by the area under the graph of the probability distribution between x=a and x=b. This is illustrated in Figure 21.3, where the shaded area gives the probability that the standard normal variate, Z, lies between z and infinity, i.e. the probability P(Z>z). The total area under the graph is equal to 1, and because of the symmetry of the normal distribution it follows that the area of any one half is equal to 0.5. For any normal... 

Figure 21.3 The standard normal distribution curve. The shaded area gives the probability that the standard normal variate, Z, lies between z and infinity, i.e. P(Z>z).

This resembles the square of the standard /-ratio for testing the hypothesis that p — 0. It would be exactly that save for the absence of a degrees of freedom correction in v. However, since we have not estimated p with x in fact, LM is exactly the square of a standard normal variate divided by a chi-squared variate over its degrees of freedom. Thus, in this model, LM is exactly an F statistic with 1 degree of freedom in the numerator and n degrees of freedom in the denominator. 

Compared to spectra obtained in the mid-infrared region, NIR spectra contain fewer, less resolved, peaks. Due to scattering and other effects, a set of NIR spectra on similar samples often exhibits constant baseline offsets from one to the next. To eliminate these baseline offset differences, reduce (but not eliminate) scattering effects, and increase the resolution of neighboring peaks, first- or second-deriva-tization is often applied to NIR spectra prior to their use in calculations. Other preprocessing techniques, such as standard normal variate (SNV) or multiplicative scatter correction (MSC), may be applied to more effectively reduce scattering effects that arise from particle size differences among samples.36... 

Multiplicative Scatter Correction (MSC) and Standard Normal Variate (SNV) Transforms... 

Two closely related methods — multiplicative scatter correction (MSC) [9] and standard normal variate (SNV) transforms [10] — are discussed in this section. MSC... 

FIGURE 4.9 Illustration of standard normal variate (SNV) preprocessing, (a) NIR reflectance spectra of 20 powdered samples of microcrystalline cellulose, (b) Same NIR reflectance spectra after SNV preprocessing, revealing differences in moisture content. 

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