After the simulations were run, the samples were sorted according to PPD and represented as scatterplots alongside the probability distribution
of the PPD.
The rth moment of a discrete probability distribution
about X = 0 is defined by
In probability theory, a log-normal distribution is a continuous probability distribution
of a random variable whose logarithm is normally distributed.
The probability distribution
of [N.sub.PM] for selected scenarios (FFS, PSR) and initial scenarios (short for OPTI) are shown in Fig.
Caption: Figure 4: Probability distribution
of normal force chains.
Apart from the joint probability distribution
, copulas are also able to establish conditional probability distributions
In order to display the space probability distribution
, we will transform (15) from original spherical coordinates to the popular Cartesian coordinates through the coordinate transformations r = [square root of ([x.sup.2] + [y.sup.2] + [z.sup.2])] and cos [theta] = z/r and then obtain the corresponding space probability distribution
[rho](x, y, z).
According to the statistics, it is found that the probability distribution
of displacement efficiency follows the normal distribution N([mu], [[sigma].sup.2]), where [mu] is the mean of the normal distribution and [sigma] is the standard deviation of the normal distribution.
Then, the joint probability distribution
is given by applying probability multiplication and additive rules:
First, in terms of definitions, we follow the ecological literature, defining diversity as the interplay of "richness" and "evenness" in a probability distribution
. Richness refers to the number of different diversity types in a system.
The Monte Carlo method simulates the full system many times, each time randomly choosing a value for each variable from its probability distribution
A probability distribution
is a statistical model that shows the possible outcomes of a particular event or course of action as well as the statistical likelihood of each event.