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