If you know the cumulative distribution function (CDF) of a probability distribution, then you can always generate a random sample from that distribution.

However, one technique stands out because of its generality and simplicity: the inverse CDF sampling technique. In my next blog post I will show how to graph the PDF and CDF for a distribution that is not built into SAS.There are many techniques for generating random variates from a specified probability distribution such as the normal, exponential, or gamma distribution. You can implement the CDF by using the QUAD subroutine, but you can use the method in this post when you only need a quick-and-dirty approximation to the CDF. You might be asking the same question that my former math students would ask: 'When will I ever use this stuff?' One answer is to use the approximation when you are computing the CDF for a distribution that is not supported by the SAS CDF function. The graph shows that the approximation is within ±5e-5 of the values from the CDF function. Title 'Difference between Normal CDF and Aproximate CDF'

* for distributions on, correct by adding constant */ĬDF = cdf('Normal', x) /* gold standard */ĬDFApprox = CumTrapIntegral(x, pdf) /* cumulative sums */ĬDFAdd = cdf('Normal', -3) /* integral on (-infinity, -3) */ĬDFApprox = CDFAdd + CDFApprox` /* trapezoidal approximation */ For example, the following statements compare the values of the standard normal CDF on with the cumulative trapezoidal sums: Namely, if you are approximating a cumulative distribution on the interal, you need to add the CDF value at a to the values returned by the CumTrapIntegral function. However, for distributions that are defined on the whole real line, you need to make a small modification to the algorithm. The lognormal distribution is exactly zero for x < 0, which means that the integral from minus infinity to 0 is zero. In general, smaller step sizes lead to smaller errors, and the error for the trapezoidal rule is proportional to the square of the step size. This result uses PDF values with a step size of 0.05. For most values of x, CDF( x) differs from the cumulative trapezoidal approximation by less than 0.0001. The graph shows that for the lognormal distribution evaluated on, the approximate CDF differs by less than 0.001. Title 'Difference between Lognormal CDF and Aproximate CDF'

From cdf to pdf