AW: [R] numericDeriv and ecdf

[Prof Brian Ripley]

An empirical CDF is a step function: it does not have a derivative at the 
jump points, and has a zero derivative everywhere else.

What is this function `numericDerivative': do you mean `numericDeriv'?
If so, it seems to be intended for differentiable functions, and
calculates one-sided derivatives.  In your example the one-sided 
derivatives are all zero.

On Fri, 25 Apr 2003, Khamenia, Valery wrote:

> > On only ten points, what did you expect ?  Even with 1000
> > observations, estimating a density is difficult, and has
> > been the subject of a century of research.  Kernel density
> > estimates are among the most successful.  For your immediate
> > application, try  plot(density(rnorm(10)), type="l"), etc.
> 
> wait, you misunderstood me!
> 
> I'd like to see 10 or 9 points with estimated values of 
> *numerical* derivatives according to ecdf output. 
> And that's it.
> 
> Now look into output of numericDerivative in my example:
> 
> [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
> attr(,"gradient")
>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
>  [1,]    0    0    0    0    0    0    0    0    0     0
>  [2,]    0    0    0    0    0    0    0    0    0     0
>  [3,]    0    0    0    0    0    0    0    0    0     0
>  [4,]    0    0    0    0    0    0    0    0    0     0
>  [5,]    0    0    0    0    0    0    0    0    0     0
>  [6,]    0    0    0    0    0    0    0    0    0     0
>  [7,]    0    0    0    0    0    0    0    0    0     0
>  [8,]    0    0    0    0    0    0    0    0    0     0
>  [9,]    0    0    0    0    0    0    0    0    0     0
> [10,]    0    0    0    0    0    0    0    0    0     0
> 
> What could you say now?
> 
> With kind regards,
> Valery A.Khamenya
> ---------------------------------------------------------------------------
> Bioinformatics Department
> BioVisioN AG, Hannover
> 
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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