Normal probability scale

The cumulative percentage points can be plotted on a distorted %-axis (so-called normal probability scale ) that yields a straight line for perfectly ND data. 

Wu, Ruff and Faethl249 made an extensive review of previous theories and correlations for droplet size after primary breakup, and performed an experimental study of primary breakup in the nearnozzle region for various relative velocities and various liquid properties. Their experimental measurements revealed that the droplet size distribution after primary breakup and prior to any secondary breakup satisfies Simmons universal root-normal distribution 264]. In this distribution, a straight line can be generated by plotting (Z)/MMD)°5 vs. cumulative volume of droplets on a normal-probability scale, where MMD is the mass median diameter of droplets. The slope of the straight line is specified by the ratio... 

Plot of a sieve analysis of a sample of run-of-bank sand is shown in Figure 7.9 by the segmented line labeled stock sand. This sample may or may not meet the required effective size and uniformity coefficient specifications. In order to transform this sand into a usable sand, it must be given some treattnent. The figure shows the cumulative percentages (represented by the normal probability scale on the ordinate) as a function of the increasing size of the sand (represented by the size of separation on the abscissa). 

Figures 62.8, 62.9, 62.10 show the data for generator fan failure plotted on exponential, normal and log normal hazard paper respectively. The exponential plot is a reasonably straight line which indicates that the failure rate is relatively constant over the range of the data. It should be noted that the reason the probability scale on the exponential hazard plot is crossed out is because that is not the proper way to plot data. (This will be discussed later.) The normal plot is curved concave upward which...

The first is to normalize the data, making them suitable for analysis by our most common parametric techniques such as analysis of variance ANOYA. A simple test of whether a selected transformation will yield a distribution of data which satisfies the underlying assumptions for ANOYA is to plot the cumulative distribution of samples on probability paper (that is a commercially available paper which has the probability function scale as one axis). One can then alter the scale of the second axis (that is, the axis other than the one which is on a probability scale) from linear to any other (logarithmic, reciprocal, square root, etc.) and see if a previously curved line indicating a skewed distribution becomes linear to indicate normality. The slope of the transformed line gives us an estimate of the standard deviation. If... 

In some cases, the data describing the actual state and their recent history are compared with so-called reference patterns these are data from historical experiments or runs which an expert has associated with a typical physiological state. A physiological state is recognized either if the actual constellation matches any one of the reference sets best - in this case, there is always an identification made - or if the match exceeds a pre-defined degree of certainty, e.g. 60% - then it can happen that no identification or association is possible with a too high limit selected. The direct association with reference data needs normalization (amplitude scaling) and, probably, frequency analysis in order to eliminate dependencies on (time) shifts, biases or drifts. 

Apparent from Fig. 24 is the self-similarity of the curves for molecular adsorption and dissociative adsorption which Nolan et al. argues provides strong evidence that both processes occur via a similar initial step, specifically, a molecularly adsorbed precursor. Further, the adsorption probability at 71 = 77 K appears to scale with normal energy, mirroring the normal energy scaling of the dissociative probability curve. 

Probability plot is presented here to verify the correctness of data. In probability plots the vertieal seale on the graph resembles the vertical scale found on normal probability distribution. The horizontal axis is a linear scale. The line forms an estimate of the eumulative distribution funetion (CDF) for the population from which data are drawn. An example for PTl series is shown in Figure 6. 

The summer of 1983 provided a rehearsal for the potential doubled CO2 effect. Temperature was above normal and precipitation below normal on scales not unlike those predicted by models of the doubled CO2 effect, or of conditions typical of mid-twenty-first century if other absorbers are included. In 1983 corn yields were halved (by reference to the previous crop year). About half this reduction was probably due to the hostile climate. Winter wheat was adversely affected in some areas, but escaped the worst effects of the summer drought, because of early harvesting dates. Spring wheat was badly affected in many areas. Thus a natural rehearsal of future events appeared to confirm the pessimistic estimates of the Abrahamson forum. 

Figure 3. (Left) The measured scaling exponents q v(q) (joined by dot-dashed straight lines) of the moments of the displacement Ax, as a function of the order q. The dashed line corresponds to 0.65 q while the dotted line corresponds to q 1.04. (Right) The normalized probability distribution function P(Ax(t)/a) versus Ai = Ax/a (a — exp(ln Ax(/ )) for the three times 0=500 (circles), + — 2 (diamonds) and / = 2/ (squares). The dashed line represents the Gaussian function.

Strong anomalous diffusion is also highlighted by the normalized probability densities P(Ax, t) at different times that do not collapse onto a unique curve [see Fig. 3 (right)], suggesting that the scaling property, Eq. (19), does not hold. 

Figure 5. (Color online) Comparison of the ordering obtained for the liquid phase by means of MD (a,b) and RMC (c,d) for the first four molecules surrounding a central one (a MD,c RMC), and for the next four molecules (b MD, d RMC). The color scale represents the normalized probability of finding the molecule at a given position (P((f),cos(B))/Pma. ...

Figure A3.9.10. The dissociation probability for O2 on W(110) [101] as a function of the normal energy, (upper). Tg = 800 K 0 ( ) 0°, (i) 30° ( ) 45° and (O) 60° The normal energy scaling observed can be explained by combining the two surface corrugations indicated schematically (lower diagrams).

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