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How to specify a discrete probability density function?
To specify a discrete probability density function, you provide a table of the specific values of the random variable along with the corresponding probability: Abaqus/Explicit will renormalize the specified probabilities to ensure that they sum up to 1.
Is the probability density of a PDF always zero?
There is an important subtlety here: a probability density is not a probability per se. For one thing, there is no requirement that p(x) ≤ 1. Moreover, the probability that x attains any one specific value out of the infinite set of possible values isR always zero, e.g. p(x)dx = 0 for any PDF p(x).
How can you estimate the density of a random variable?
Once identified, you can attempt to estimate the density of the random variable with a chosen probability distribution. This can be achieved by estimating the parameters of the distribution from a random sample of data. For example, the normal distribution has two parameters: the mean and the standard deviation.
When to use a piecewise probability density function?
A piecewise linear probability density function can be used to approximate general distributions that are not well represented by the other PDF forms discussed above. With a piecewise linear probability density function, you specify PDF values at discrete points.
How to define a probability density function in Abaqus?
Abaqus/Explicit supports uniform, normal (Gaussian), log-normal, piecewise linear, and discrete probability density functions. To define a probability density function, you must assign it a name and specify its type.
When to use a log normal density function?
Log-normal distributions (shown in Figure 4 ) are used in describing many natural phenomena. They are commonly used to describe particle size distributions in soils. The following function describes a log-normal probability density function: σ 2] x > 0 0 otherwise.