[R] Simulating mid-points from a defined range

[Brian Smith]

Okay, I think I found the reason. This is due to accumulation of nine
5s in the cumsum. Thanks again for the elegant solution.

But I wonder, if the solution is simple then what is the significance
of the Research paper by Bentley and Saxe naming “Generating sorted
lists of random numbers” which Richard mentioned?

On Wed, 4 Jun 2025 at 17:54, Brian Smith <briansmith199312 using gmail.com> wrote:
>
> Hi Peter,
>
> Could you please help me to understand what is the basis of choosing
> 55 in runif(10,0,55))?
>
> Thank you!
>
> On Wed, 4 Jun 2025 at 02:45, peter dalgaard <pdalgd using gmail.com> wrote:
> >
> > Can't you just generate 10 values in (0,55), sort them, generate the distances, add 5 and cumulate?
> >
> > > x <- sort(runif(10,0,55))
> > > d <- diff(x)+5
> > > cumsum(c(x[1],d))
> >  [1] 12.27815 21.21060 26.37856 36.03812 41.97237 57.02945 67.86113
> >  [8] 75.74085 81.28533 98.30792
> >
> >
> > > On 3 Jun 2025, at 09.21, Brian Smith <briansmith199312 using gmail.com> wrote:
> > >
> > > Hi Richard,
> > >
> > > Thanks for your insight.
> > >
> > > As I mentioned in one of my earlier emails to the group, I imposed a
> > > constraint of accuracy up to two decimal places in order to obtain a
> > > finite set of possible values. For instance, if I were to round values
> > > to zero decimal places, the number of unique sequences that could be
> > > generated would be strictly finite and quite limited. Therefore, I
> > > chose a precision of two decimal places to allow for a larger but
> > > still finite number of possibilities.
> > >
> > >
> > > Now, my question is: how can this accuracy constraint be imposed effectively?
> > >
> > > Is the only practical method to generate samples, round each to two
> > > decimal places, and then check for duplicates to ensure uniqueness? If
> > > so, I’m concerned this might be inefficient, as many samples could be
> > > discarded, making the process time-consuming.
> > >
> > > Is there a better or more efficient way to directly enforce this
> > > constraint while generating the values?
> > >
> > > ________________________________
> > >
> > > Additionally, could you please elaborate on your suggestion regarding
> > > imposing minimum gap constraints by subtracting and then adding back
> > > certain gaps?
> > >
> > >
> > > For example, based on your earlier guidance, one possible sequence I
> > > obtained is:
> > >
> > >
> > > 10.07181, 14.49839, 14.74435, 18.75167, 42.70361, 55.79623, 63.40264,
> > > 68.62261, 92.49899, 98.29308
> > >
> > >
> > > Now, I’d like to post-process this sequence to enforce a minimum
> > > difference constraint of, say, 5 units between values (including both
> > > lower and upper bounds).
> > >
> > > What would be the appropriate way to modify the sequence to impose
> > > this kind of constraint?
> > >
> > >
> > > Many thanks for your time and insight.
> > >
> > > On Tue, 3 Jun 2025 at 10:42, Richard O'Keefe <raoknz using gmail.com> wrote:
> > >>
> > >> PS I forgot about the weird gaps requirement.
> > >> What you do is subtract the gaps off and then add them back.  I hope that is clear.
> > >>
> > >> On Sun, 1 Jun 2025 at 6:52 AM, Brian Smith <briansmith199312 using gmail.com> wrote:
> > >>>
> > >>> Hi,
> > >>>
> > >>> Let say I have a range [0, 100]
> > >>>
> > >>> Now I need to simulate 1000 10 mid-points within the range with
> > >>> accuracy upto second decimal number.
> > >>>
> > >>> Let say, one simulated set is
> > >>>
> > >>> X1, X2, ..., X10
> > >>>
> > >>> Ofcourrse
> > >>>
> > >>> X1 < X2 < ... <X10
> > >>>
> > >>> I have one more constraint that the difference between any 2
> > >>> consecutive mid-points shall be at-least 5.00.
> > >>>
> > >>> I wonder if there is any Statistical theory available to support this
> > >>> kind of simulation.
> > >>>
> > >>> Alternately, is there any way in R to implement this?
> > >>>
> > >>> ______________________________________________
> > >>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > >>> https://stat.ethz.ch/mailman/listinfo/r-help
> > >>> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> > >>> and provide commented, minimal, self-contained, reproducible code.
> > >
> > > ______________________________________________
> > > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible code.
> >
> > --
> > Peter Dalgaard, Professor,
> > Center for Statistics, Copenhagen Business SchoolSolbjerg Plads 3, 2000 Frederiksberg, Denmark
> > Phone: (+45)38153501
> > Office: A 4.23
> > Email: pd.mes using cbs.dk  Priv: PDalgd using gmail.com
> >