Shape parameters of the beta distribution can be back calculated from this torque ratio to determine the

probability density function that statistically describes the plate motion.

However, the generation of a

probability density functions as proposed by the authors required a large amount of training data that were different from the actual test data.

Without loss of generality, v and [Z.sub.k])([y.sub.k]) are independent; thus, the

probability density function of I([y.sub.k]) can be calculated as

Caption: Figure 6: Order parameter changes with temperature (the illustration shows the distribution of

probability density functions of order parameters).

In Figure 3, the left Figure 3(a) shows the average energy consumption and its standard deviation for different scenarios, and Figure 3(b) shows the

probability density function for each scenario.

Caption: Figure 2: Difference of

probability density function: [x.sub.10] = 110, [x.sub.20] = 100, [[bar.[sigma]].sub.1] = 0.25, [[bar.[sigma]].sub.2] = 0.15, [bar.[rho]] = -0.5, and t - [t.sub.0] = 1.

After the strain is regarded as a random variable, the following

probability density function is used to describe the mesoscopic element failure behavior:

Mathematically, let [mathematical expression not reproducible] and [mathematical expression not reproducible], where F is the cumulative function of the

probability density function f(y; [mu], [THETA]); then the randomized quantile residuals for [y.sub.i] are

The calculated results show that the

probability density function model (PDFM) more accurately reflects measurement data than the log-law model.

Plots for the cumulative distribution function (CDF),

probability density function (PDF), hazard function were also presented in this article.

In order to analytically evaluate ASEP for applied modulation format, expression for conditional SEP (conditioned over fading statistics which impairs the communication) should be averaged over the

probability density function (PDF) of the fading channel amplitude.

If the distribution G (x) has density g (x) the class will have a

probability density function (pdf) given by