PDF estimation from first tail data points
I have the following problem.
I want to estimate the pdf of the life time of a component.
I have data from all components that have failed before time t1.
I also know the fraction of components that have failed before time t1.
So: I know for each component that failed before time t1 how many days d it was used before failure (d<t1), and I know that out of n components m failed before the warranty time had elapsed (m/n ~ 10%).
How can I use this information to estimate the probability of failure as a function of time?
We can assume that the function will only have one peak.
Re: PDF estimation from first tail data points
Have you looked at the exponential distribution or other distributions based on assumptions for particular processes with failure rates?
If every failure doesn't depend on the failures happened before (or happen after) then look at the exponential distribution and related distributions for failure processes.