Talk:Rankit

message: In my last edit summary, I should have said it's a normal probability plot regardless of whether the underlying distribution is normal.  Rankits are based on a normal distribution.  Normal probability plots are used in order (among other things) diagnose non-normality! Michael Hardy 23:49, 10 February 2006 (UTC)
replies: text: It is certainly something that virtually all statisticians use all the time.  Normal probability plots are standard fair.  The individual numbers may often be called "expected normal order statistics" or the like, rather than "rankits".  In the graduate program in statistics at the University of Minnesota, use of the term is widespread, perhaps because one of the professors studied under Chester Bliss.  I think having a short term rather than a long descriptive phrase is useful Michael Hardy 21:02, 3 November 2006 (UTC)
thread_title:  Early comments 

message: Should the article title be Rankit or Normal probability plot ? 
* Rankit just scored 40,100 hits on Google
* "Normal proability plot" scored 93,900 hits
What do others think?  DFH 18:53, 29 January 2007 (UTC)
replies: text: Well, I recently needed to use this page.  I searched for a probability plot, and saw that the normal probability plot redirected to here (I created a redirect for probability plot to this page too, for the time being).  I think the appropriate page name should be "normal probability plot" over "rankit" simply because I have never heard of the term rankit in any statistics course I have had, while I have used normal probability plots extensively.  Jason Smith 05:57, 21 February 2007 (UTC)

text: I have put articles at Probability plot and Normal probability plot based on the public domain counterparts at NIST. Does anyone feel like merging Rankit into Probability plot? Btyner (talk) 15:48, 16 February 2008 (UTC)
thread_title:  Article title? 

message: Here's a biographical reference:
* "Chester Ittner Bliss, 1899-1979", William G. Cochran, David J. Finney, in Biometrics, Vol. 35, No. 4 (Dec., 1979), pp. 715-717.
DFH 19:13, 29 January 2007 (UTC)
thread_title:  Chester Bliss 

message: The article says that one can plot the Q-Q plot with quantiles of any other distribution. Why is this not possible for the P-P plot? One should think that this is possible for the P-P plot also.
Vivek 08:29, 29 May 2007 (UTC)
thread_title:  Is the Q-Q plot superior to the P-P plot? 

message: Nowhere on the page is it explained how one can calculate the expected order statistics, and it should be. 71.64.105.56 (talk) 23:55, 26 September 2009 (UTC)
replies: text: Good point.  Some crude methods are obvious, but efficient methods that you would want to use in practice are more work to discover.  This is certainly out there in the literature somewhere. Michael Hardy (talk) 20:13, 5 April 2010 (UTC)
thread_title:  How are the rankits calculated? 

message: The rankits can be estimated using a number of formula although all are approximations to the real thing - for example the sorts of values discussed above.
The key here is the word Expected ie 'Expected values of the Normal order statistics'. 
That 'Expected value' corresponds to the mean and there is no simple formula for this. 
The correct formula involves an integral of products of the powers of the Normal and cumulative Normal curves taken to various powers. 
It goes something like this according to Teichroew 
:E(x_j;N) = {N! \over (j-1)! (N-j)!} B(j-1,N-j),
where 
:B(m,n)=  \int_{-\infty}^{\infty} x f(x) F(x)^m(1-F(x))^n  dx,
and where f(x) and F(x) are the Normal distribution function in density and cumulative form.
These have been calculated and tabulated in a number of places and one example for N=1 to 20 is Tiechroew 
::More can be found on this inside Wikipedia and in other sources using a search on 'expected values of the Normal order statistics'
It is relatively easy to calculate the values of these corresponding to the median (ie not the expected or mean value) and a formula involving the inverse Beta distribution is commonly used ie for Excel write 
:=NORMSDIST(BETAINV(0.5,i,n+1-i))  
where the constant 0.5 forces the median value, n is the number of order statistics being calculated, and i is the particular one. So i = 1,2,3,...,n.  
From that inverse beta approach one can also calculate the positions of the various percentiles by changing the 0.5 value.
There are a number of approximations to the expected values of the normal order statistics  
:=NORMSDIST((i-k)/(n+1-2*k)) 
where 
:i and n are the same as before and k is a constant that takes on values between 0 and 0.5. 
Are you sure you don't mean NORMSINV in the equation above?  — Preceding unsigned comment added by 206.173.46.67 (talk) 20:10, 16 November 2011 (UTC)
thread_title:  Values for the Rankits