There is a sample of n values that are the first n largest values of a population. Is there a way of getting any statistics such as mean or dispersion from such pieces of information, provided the population is normally distributed with its size either known or unknown?
You could consider the data as being drawn from a truncated normal distribution, where the truncation point lies at the (unobserved) (n+1)-th point. You can model this in a Bayesian framework, marginalizing over the uncertainty about what the truncation point is. You probably have to provide the model with a rather informative prior for the truncation point to be able to get a sensible estimate of the mean and variation in the source population.
Good idea, may be with potential application.
It is someway analogues to the ranked set sampling. For estimation of any statistics, you must also account the position value (rank).
Thanks.
Finding dispersion, even from such a sample, should not be a problem. Having information about 'normal distribution' of population is a plus point. 'Marks secured by top n-students in one examination' could be an example of 'known population size case'. RG-Scores of top ranked Institutes/ universities could be another example.
We can find dispersion. Other information can also be derived (by looking at the distribution pattern of top-n items/ units).
Can we also infer from the inter-unit distances?
Sample data:
Look at the following data on Total RG scores of Institutes
(which is part of my work, available in RG):
.........................................................................................................................
As on Dt.25.02.2014 (at 1 PM IST), we find the number of leading Institutes/ Universities of the world, as per the latest RG-Score:
Number of Institutes/ Universities with >15000 Total RG Score = 267
Number of Institutes/ Universities with >10,000 Total RG Score = 428
Number of Institutes/ Universities with >5000 Total RG Score = 793
Number of Institutes/ Universities with >1000 Total RG Score = 2630
As we find from the above statistics, hardly 800 Institution/ Universities are there having scores above 5000.
When we look at the leaders list, we can have it separately as per ‘Total RG Score’ or ‘Total Impact points’, as: (a): Top-10 on Total Impact points (Institutes with present total score)
1.University of Washington Seattle 357,271.34
2.University of California, San Francisco 301,491.34
3.National Institutes of Health 295,197.56
4.Harvard Medical School 291,530.00
5.Stanford University 283,821.38
6.Johns Hopkins University 270,565.62
7.University of Toronto 252,072.77
8.University of California, Los Angeles 239,563.53
9.University of Michigan 238,110.48
10.University of Wisconsin, Madison 217,656.78
(b): Top-10 on Total RG Score: (Institutes with present total score)
1.Chinese Academy of Sciences 92,192.73
2.University of São Paulo 83,630.03
3.National Research Council 74,289.07
4.French National Centre for Scientific Re... 73,175.98
5.University of Michigan 72,147.95
6.Russian Academy of Sciences 71,792.26
7.Karolinska Institutet 64,030.35
8.University of Washington Seattle 60,097.24
9.National Institutes of Health 60,082.38
10.University College London 58,759.75
[Source: https://www.researchgate.net/institutions/worldwide?order=rgScore&method=total&facility=University_of_Oxford ]
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