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Abstract:
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Let $\left\{V_{j},j=0,1,2,\ldots\right\}$ be a random sequence of integers between $0$ and $2^{w}$, inclusive. For $j\geq1$, $U_{j}=V_{j}/2^{w}$ may be viewed as the $j^{th}$ sample from a continuous uniform distribution on $\left[0,1\right]$, with accuracy to within $2^{-w}$. The members of the set $\left\{U_{j},j=1,2,\cdots\right\}$ are called values from a \emph{Bounded Accuracy Continuous Uniform Variate (BACUV) On } $\left[0,1\right]$, and the bounded accuracy is $2^{-w}$. The purpose of this paper is to define policy on how such $V_{j}$ (therefore $U_{j}$) may be optimally chosen in a given context. After defining the methods for calculating $U_{j}$, a bounded accuracy continuous uniform variate $W_{j}$ on any other real interval $\left[\alpha,\omega\right]$ (with $\omega>\alpha$) may be constructed from the $U_{j}$ by $W_{j}=\left(\omega-\alpha\right) U_{j}+\alpha$.
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