# Hypothesis testing over probability density function

I have PDF of time variable, and I'd like to create statistical test in order to decide if new data point derived from my distribution.

Say I'm setting a p-value of alpha. My question is how should I find my "rejection area". Should I search for a c (cutoff) value which all points' (e.g., minutes) densities above this cutoff summarised into (1-alpha) or should I do the search of this cutoff over the points' probabilities (in that case I'll compute the probability over minutes' interval)?

Hope my question is clear. Thank you in advance!

• Thank you very much. It is a very good answer. I'd like to ask you one more thing. My data is actually bounded (time of the day - continuous but bounded) and multi-modal.. so, prectically, I should: 1. caculate the probability of (for examle) each minute during the day from my pdf; 2. Sorting those probabilities in descending order; 3. Summarised the probabilities until I get 95% (assume the acceptable long-run error rate is 5%); 4. Set my cutoff as the probability of the "first point left out".. am I right? – staove7 Apr 26 '17 at 17:09