I have 19 data points and I found that inverse gamma distribution best fits my data. Now, I got one more data point (i.e. 20th data point) and i want to check that if this data point lies on the extreme right side of my distribution (on the tail of the distribution). The main purpose of this analysis is to find out if this new point lies somewhere in the middle of distribution or as a second option, if 95% of the values are less than this newly added data point. Can anybody recommend any appropriate statistical test for this situation. I am more comfortable using R so if anybody can recommend something in R, I would really appreciate that.
You have only 19 values so I assume you have little confidence in the underlying distribution. With just 19 values to see if this new point is higher than 95% of exist values you just see if it is higher than the 19 values that you already have. It is unclear why you would be doing this. You might share the reason with folks. ps. The "somewhere in the middle" bit is so vague I assume if you want anyone to address that you will start a new question.
Hi Huma,
I would suggest:
Did you try to find the mean of Gama Dist? if yes, is there sig differences between 20 point and mean best on the 19 values?
Regards
Ahmad Al-shallawi Yes i do have the mean and standard deviation of gamma distribution and thats what i am trying to find that if this 20th point is significantly different from mean and SD of distribution. Not sure, which test should i use? Any recommendations?
You have 19 data points. If this is the only information that you are using to say that these data have been drawn from a particular distribution, this little information. Since you seem very confident I assume you have other information. Sharing this will be helpful.
Also, you say you have the mean and SD of this population distribution. Say how? If you just have estimates of them based on a small sample, do not say you have the mean and sd. Provide the uncertainty. But, again, given your confidence I assume you have this information from something other than the 19 cases. It again will be helpful if you share this information.
Daniel Wright I completely understand your point. I agree that 19 data points are not enough for such statistics. I am just doing it for the practice to find out if any analysis like this one is possible or not so that when I have more data in hand (in the near future), I will have an optimized methodology to detect the likelihood of a new test data point. My main focus will be to test if any specific data point follows that fitted distribution or not.
This is not possible. The only thing you can say is that a point with a negative value is not from an inverse gamma distribution.
Your problem makes sense only if you have an alternative distribution, so that you can say of which alternatives the observed value is more likely.
Most humans would have said in their original question that this was just for practice.
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