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My problem is that I need to do an interpolation. Eventually, I will work on the hazard rate, but I do not know if it is better to interpolate the CDF or the hazard rate. Let me explain better.

I've a CDF evaluated at certain points. I numerically differentiate it over the points (diff function in R) to get the pdf. I'm interested in computing the inverse hazard rate ($\frac{1-F(x)}{f(x)}$) and to have it over a broader set of values $y$.

Is it better to interpolate the CDF $F(x)$ over the broader set of values $y$, (that is, interpolate $F(x)$ over $y$ and then compute the pdf and inverse hazard rate over $y$), or to interpolate the hazard rate directly in the end? Also, which is the best interpolation procedure?

Thank you.

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    $\begingroup$ Why are you interested in estimating the inverse hazard rate? This will help guide an answer. $\endgroup$ – Cliff AB May 29 '16 at 1:46
  • $\begingroup$ I'm estimating a model by taking the GMM of the first order conditions and the inverse hazard rate enters linearly in the FOC. $\endgroup$ – tony May 29 '16 at 7:16
  • $\begingroup$ When you say you have a CDF evaluated at several points, do you mean the Kaplan Meier curves (or if not censored, EDF?) Because then using numerical differentiation is going to be very problematic. If you are using a parametric model, this is very reasonable. $\endgroup$ – Cliff AB May 29 '16 at 20:55
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For failure-time modeling it's appropriate to model (interpolate) the hazard rate, since most tests are based on the hazard rate. However, for general probability distribution fitting, it's better to fit the cdf. This is called "empirical CDF fitting".

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