After the simulations were run, the samples were sorted according to PPD and represented as scatterplots alongside the

probability distribution of the PPD.

Probability Distribution Characteristics of the Rock Material

The rth moment of a discrete

probability distribution about X = 0 is defined by

Heitsch and Romisch [15] 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 [14], 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 [5], 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.