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6
votes
1answer
115 views

Correlation between an observation and its rank in a random sample

Suppose $X_1,X_2,\ldots,X_n$ are i.i.d random variables with an absolutely continuous distribution. We say the observation $X_i$ has rank $R_i$ if $$X_i=X_{(R_i)}\quad,\,i=1,2,\ldots,n,$$ where $X_{(...
0
votes
1answer
51 views

Let $\mathbf{R}^{*}$ be rank vector of a random sample and $V=R_{1}^{*}-R_{N}^{*}$. Then $\mathsf{P}(V=k)= \frac{N-|k|}{N(N-1)}$

Let $Z_{1},\ldots, Z_{N}$ be i.i.d. continuous random variables with rank vector $\mathbf{R}^{*}=(R^{*}_{1},\ldots,R_{N}^{*})$, where $R_{i}^{*}$ denotes the rank of $Z_{i}$ among $Z_{1},\ldots, Z_{N}$...
2
votes
1answer
674 views

Rank data from 1 to N (N may not be equal to number of elements in the dataset)

I calculate percentile ranks based on the method at http://www.psychstat.missouristate.edu/introbook/sbk14m.htm I need to assign ranks to a dataset where ranks are ...