Average kurtosis

In summary, the height distribution of surface roughness, characterized by the skewness and kurtosis, may present a significant influence on certain performances of mixed lubrication, such as the real contact area, the load carried by asperities, and pressure distribution, while the average film thickness and surface temperature are relatively unaffected. 

Fig. 21 —The changes of lubrication properties with the kurtosis, simulated at cr=0.1 /xm and different values of skewness, (a) Contact area ratio versus skewness, (b) Load ratio versus skewness, (c) Maximum pressure versus kurtosis. (d) Maximum temperature versus kurtosis. (e) Average film thickness versus kurtosis.

Fig. 22—The change of contact area ratio and average film thickness with skewness, simulated at o-=0.1 /u.m and for different kurtosis. (a) Area ratio versus skewness and (b) average film thickness versus skewness.

This technique assumes a Gaussian spreading function and thus does not take into account skewness or kurtosis resulting from instrumental considerations. It can, however, be modified to accommodate these corrections. The particle size averages reported here have been derived usino the technique as proposed by Husain, Vlachopoulos, and Hamielec 23). 

The first four terms called, respectively, the average (or expectation value), variance, skewness, and kurtosis, are equal to... 

Besides the calculation of average molecular weights, several other means of characterizing the distribution were produced. These include tables of percentile fractions vs. molecular weights, standard deviation, skewness, and kurtosis. The data for the tables were obtained on punched cards as well as printed output. The punched cards were used as input to a CAL COMP plotter to obtain a curve as shown in Figure 3. This plot is normalized with respect to area. No corrections were made for axial dispersion. 

Fig. 22a and b. Dependence of the measured elution volume V = VD (in cm3, Fig. a), and of the standard deviation ctd (in cm3), skewness yD, and kurtosis 5D (Fig. b) on the weight-average of the polymerization degree Pw of very narrowly distributed polystyrene samples (BW-middle fractions of the anionic polystyrene standards), injected into the PDC-column 3) at 28 °C where the resolution of the column can be neglected in the Pw-range as indicated (polystyrene/cyclohexane, theta temperature 34 °C)... 

The average value and variance of tc2==C) are, of course, much smaller than those for tni C2, but its distribution is far from normal (high standardized skewness and kurtosis). The restriction of the first atom of R1- 5 substituents to carbon significantly reduces the variance and the range of this parameter and makes the distribution closer to normal. 

Whereas the mean correlation coefficient is significantly lower in the arbitrary data set, the mean skewness and mean kurtosis are similar. Though the latter values do not indicate clearly a difference between the data sets — they just indicate a similar symmetry and flatness of distribution — the deviations from the average behavior describes properly the diversity of the data set The average deviations in skewness and kurtosis are about twice as high in the arbitrary data set as those of the benzene derivatives. The ASD and the combination of deviations in correlation coefficients, skewness, and kurtosis provide the most reliable measure for similarity and diversity of data sets. 

Geometrical parameter Average Mode Variance Standard error maximum range skewness kurtosis... 

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