sigma from range

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2 total messages Started by Dave Marchette Fri, 20 Nov 1992 16:12

#712

Author: Dave Marchette
Date: Fri, 20 Nov 1992 16:12

15 lines
866 bytes

Here's a simple question, I wonder if anyone can help with:

Let x1,...,xn be iid normal 0, sigma, and let x(1),...,x(n)
be the order statistics.  Assume that only n and x(n)-x(1)
are known.  That is, only the number of points and the total
spread of the points is known.  What is the appropriate estimate 
of sigma?

Thanks for any help,

David Marchette
NRaD 
Code 421
San Diego, Ca  92152
marchett@antares.nosc.mil

Re: sigma from range

#718

Author: Peter Wright
Date: Sun, 22 Nov 1992 22:45

28 lines
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In <1992Nov20.161226.27020@nosc.mil> marchett@antares.nosc.mil (Dave Marchette) writes:

>Let x1,...,xn be iid normal 0, sigma, and let x(1),...,x(n)
>be the order statistics.  Assume that only n and x(n)-x(1)
>are known.  That is, only the number of points and the total
>spread of the points is known.  What is the appropriate estimate 
>of sigma?

An unbiased estimator of sigma is the range divided by a constant (which is
a function of n). Unfortunately there is no nice closed expression for the
constant, since it is the solution to an integral equation. However the
constant is tabulated in lots of places, especially in quality control texts.
Some refs:

Pearson E.S. (1942) "The Probability Integral of the Range ...", 
	Biometrika, 32, p.301-310.
Dixon, W.J. & Massey, F.J. (1969) "Introduction to Statistical Analysis",
	McGraw-Hill, p.136, p.486.
Duncan, A.J. (1986) "Quality Control and Industrial Statistics", Irwin,  
	p.481, p.1005.
Montgomery, D.C. (1991) "Introduction to Statistical Quality Control", Wiley,
	p.204, p.A-15.

--
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  PETER WRIGHT, School of Math Sc,      |  Email: peterw@zen.maths.uts.edu.au
  University of Technology, Sydney      |  Phone:      (612) 330 2243
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