Q:

Interpolation for PDF from Cumulative Distribution

How to interpolate PDF(Probability Distribution Functions) from CDF (without root finding method) ?
Please tell the steps to do so.
Thanks.

A:

If you have an analytical form of the CDF, you can simply take the first derivative to obtain the PDF (for a continuous distribution). If you have numerical data points representing a CDF, you can construct a numerical approximation to the first derivative by using a finite difference method. If you're going the numerical route, you should use at least a symmetric second-order finite difference, since it's just as easy as the first-order methods.
$$
PDF(x) = \frac{CDF(x+\delta x) - CDF(x-\delta x)}{2 \,\delta x} + O(\delta x^2)
$$

