\(\text{WeibullVariate}\)

You can use the \(\text{WeibullVariate}\) function to calculate one or more random variates in a Weibull distribution.

You can use the \weibullv backslash command to insert this function.

The following variants of this function are available:

• \(\text{real } \text{WeibullVariate} \left ( \text{<k>}, \text{<}\lambda\text{>} \right )\)

• \(\text{real } \text{WeibullVariate} \left ( \text{<k>}, \text{<}\lambda\text{>}, \text{<delay>} \right )\)

• \(\text{real matrix } \text{WeibullVariate} \left ( \text{<number rows>}, \text{<number columns>}, \text{<k>}, \text{<}\lambda\text{>} \right )\)

• \(\text{real matrix } \text{WeibullVariate} \left ( \text{<number rows>}, \text{<number columns>}, \text{<k>}, \text{<}\lambda\text{>}, \text{<delay>} \right )\)

Where \(\text{<k>}\), and \(\text{<}\lambda\text{>}\) are scalar values representing the value of interest, the shape term, and the scale term respectively. The \(\text{<delay>}\) term is optional and adds a delay to the calculates variates. The \(\text{WeibullVariate}\) function is defined over the range \(k > 0\) and \(\lambda > 0\) and will generate an error, return NaN or a matrix of NaN for values for which the function is not defined.

The one and two parameter versions return a single value. The three and four parameter versions return a real matrix with dimensions determined by the \(\text{<number rows>}\) and \(\text{<number columns>}\) parameters.

The \(\text{WeibullVariate}\) function calculates random variates by transformation method using:

\[\text{WeibullVariate} \left ( x, k, \lambda, delay \right ) = delay + \lambda \left [ - \ln \left ( u \right ) \right ] ^ \frac{1}{k}\]

Where \(u\) is a random variate in a uniform distribution over the range (0, 1]. The matrix version uses SIMD instructions to improve performance.

Figure 222 shows the basic use of the \(\text{WeibullVariate}\) function.

Figure 222 Example Use Of the WeibullVariate Function