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\title{Connections between statistics, interval analysis and global
optimization}
\author{G. William Walster}

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\markright{APIC'95, El Paso,
Extended Abstracts,
A Supplement to the international journal of {\rm Reliable
Computing}\ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ }

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\begin{abstract}
There are a surprising number of connections between interval
analysis and statistics.  They include:
\begin{itemize}
	\item Classical and Bayesian sample size computations, which require
	the interval computation of:
	\begin{itemize}
		\item[$\bullet$] 
Central and Noncentral Cumulative Distribution Functions 
		(CDFs) and Inverse CDFs for test statistics, including:
		\begin{itemize}
			\item[$\bullet$] Gaussian,
			\item[$\bullet$] t,
			\item[$\bullet$] Gamma (Chi Square) and
			\item[$\bullet$] Beta (F).
     \end{itemize}\end{itemize}
  \item Parameter estimation when closed form solutions do not
	exist.
			
 \item Algorithms that depend on representing measurement errors as
	intervals.
\end{itemize}
To improve the performance of sample size computations, interval
rational function approximations are needed for the various CDFs and
their inverses.  The functional equivalent of an interval Remez
Exchange algorithm is required.
\end{abstract} 
  
\auffil{The author is a Manager with Fortran Compiler Technology,
		SunSoft, A Sun Microsystems Business,
e-mail Bill.Walster@eng.sun.com.}
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