After the simulations were run, the samples were sorted according to PPD and represented as scatterplots alongside the probability distribution
of the PPD.
Characteristics of the Rock Material
The rth moment of a discrete probability distribution
about X = 0 is defined by
Heitsch and Romisch  proposed a kind of fast forward and backward reduction to reduce the computational complexity, applying the discretization of possibility distribution instead of the initial continuous probability distribution
. A scenario optimal reduction technique, introduced by Dupacova et al , applied the Foret-Mourier distance and duality theory to compute the distance between two probability measures.
The probability distributions
of normal force chains are basically consistent for different f.
Meanwhile, the goal of the copula-based analysis of precipitation and SPEI is to obtain the conditional probability distributions
of meteorological drought given different precipitation conditions.
It is found that the graphics become compressed; that is, the space probability distributions
elongate along with the x- and y-axis and also the hole formed in the ring-shaped potentials expands towards the outside as the ring-shaped potential parameter b increases.
Similarly, the joint probability distribution
of two-dimensional random variables (X Y) can be listed as follows:
We propose to use reduced probability distributions
(RPD) to determine the number and type of modes in each arm.
In , we showed how to carry out the renormalization for discrete probability distributions
, both mathematical and empirical.
Assigning probability distributions
to the input variables
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.