Probability Distributions for the Variables Variable Type of Distribution Distribution Distribution Distribution Parameter 1 Parameter 2 Parameter 3 [t.sub.a] t Location-Scale mu: 23.153 sigma: 1.019 nu: 5.239 [t.sub.r] t Location-Scale mu: 23.220 sigma: 1.051 nu: 4.429 [V.sub.a] t Location-Scale mu: 0.127 sigma: 0.047 nu: 3.289 RH Generalized k: -0.408 sigma: 11.305 mu: 48.994 Extreme Value CLO Generalized k: 0.269 sigma: 0.075 mu: 0.774 Extreme Value MET Normal mu:1.414 sigma: 0.290 -

The Weibull distribution is one of the most important continuous

probability distributions. It was first introduced to study the issue of structural strength and life data analysis and has been successfully applied to the mechanical failures of geomaterials [20-22].

Now, we introduce the generalized discrete

probability distribution whose probability mass function is

However, the

probability distributions of [d.sub.1L] for selected scenarios and initial scenarios are shown in Fig.

As can be seen in Figure 4, the

probability distributions of normal force chains P(f) have no significant differences at four loading times and the maximum

probability distribution (P(f) = 0.2495) at 0.5 x [10.sup.-3] s is greater than the other three loading times.

Copulas can be used to combine precipitation and drought indexes and to provide conditional

probability distributions (with precipitation as the condition) between them.

It is well known that the space

probability distributions for a moving particle at the position [mathematical expression not reproducible] can be calculated by

Law of Large Numbers indicates that the limit of the frequency tends to probability; thus the choice habits of A and B can be represented as the

probability distribution of random variables X and Y:

NIST Operating Unit Physical Measurement Laboratory, Quantum Measurement Division, Quantum Optics Group Category Evaluation of

probability distributions. Designed to pair with Levenberg-Marquardt non-linear fitting algorithm.

(i) First, it is well known that, on a finite measure space, the uniform distribution maximizes entropy: that is, the uniform distribution has the maximal entropy among all

probability distributions on a set of finite Lebesgue measures [8].

Monte Carlo simulation is a method in which we assighn

probability distributions to the input variables (critical factors) and, on that basis, we calculate output variables and the probability of their occurence.

Probability distributions can be used to create scenario analyses.