Skip to content
SunSolve

Cumulative Distribution

Having clipped the PDF, SunSolve-P90 constructs a cumulative distribution function, by first scaling it such that its integral is unity, and then integrating

CDF(x)=∫−∞xPDF(x′)dx′\text{CDF}(x) = \int_{-\infty}^{x} \text{PDF}(x') dx'

such that CDF(x) extends from 0 to 1. Examples of the CDFs are shown in Figure 4.4.

Figure 4.4

Figure 4.4: Cumulative distribution functions (CDFs) of the four examples given in Figure 4.2.

Inverse CDF Construction

Section titled “Inverse CDF Construction”

Finally, the inverse CDF is determined, ICDF(R), so that entering a value R between 0 and 1 gives x.

The ICDF for a Weibull function can be determined analytically (with or without clipping). The ICDF of the other functions is determined numerically using 100 points, and x is determined by linear interpolation.