Discussing probability and statistics needed by physicists and engineers, they cover random phenomena, probability, random variables, expected values, commonly used discrete distributions, commonly used density functions
, joint distributions, some multivariate distributions, a collection of random variables, sampling distributions, estimation, interval estimation, tests of statistical hypotheses, model building and regression, and designing experiments and analyzing variance.
The kernel density function-based method is a positivity-preserving representation and can be regarded as the development of parameter-fitting method, which approximates the PSD by a superposition of weighted kernel density functions
Figure 1 show the graph of the gamma[(1 - Exp)/Exp] distribution probability density functions
and cumulative distribution, for some values of the parameters.
Caption: Figure 1: Density functions
for the MSL distributions with [lambda] = 0.6 and several values of q (a), compared with SHN and PL distribution (b).
Caption: FIGURE 16: Histogram of vehicle induced stress and probability density functions
These weights depend on kernel function that represents the probability density functions
Since one of the most common used distributions in literature is Pearson distribution, four-parameter system of probability density functions
, which is provided by Abate et al.
Throughput distribution and probability density functions
are shown on Figure 6.
Figure 7 displays these probability density functions
[phi](x) transformed to the phase plane representation defined above, p(x) = -(d/dx) ln([phi](x)/N)/N.
SUSA generates probability density functions
for each variable.
Estimation of wind energy potential using different probability density functions
. Applied Energy 2011; 88(5): 1848-56.