# [R] Fitdistrplus and Custom Probability Density

David Winsemius dwinsemius at comcast.net
Tue Nov 7 17:55:23 CET 2017

```> On Nov 7, 2017, at 6:58 AM, Eric Berger <ericjberger at gmail.com> wrote:
>
> Why not define your own functions based on d?
> e.g.
> myCumDist <- function(x) { integrate(d, lower=-Inf, upper=x)\$value  }
> myQuantile <- function(x) { uniroot(f=function(y) { h(y) - x },
> interval=c(-5,5)) }  # limits -5,5 should be replaced by your own which
> might require some fiddling

My test gave an error regarding a missing `h` function. Perhaps you meant something like:

myQuantile <- function(x) { uniroot(f=function(y) { myCumDist(y)-x },
interval=c(-5,5))\$root }

I added the \$root extraction so it now returns a numeric value instead of a list. I wondered if that might be somewhat slow, and considered the possibility of building a close aproximation that didn't require a combined integration and rootfinding operation for every value using approxfun() on a suitable range of p-values in the range [0,1]

--
David.
>
> e.g.
> d <- function(x) { exp(-x^2/2)/(sqrt(2*pi)) }  # just an example for you to
>
> Then define myCumDist, myQuantile as above and compare with pnorm, qnorm.
>
> HTH,
> Eric
>
>
>
>
> On Tue, Nov 7, 2017 at 4:22 PM, Lorenzo Isella <lorenzo.isella at gmail.com>
> wrote:
>
>> Dear All,
>> Apologies for not providing a reproducible example, but if I could, then I
>> would be able to answer myself my question.
>> Essentially, I am trying to fit a very complicated custom probability
>> distribution to some data.
>> Fitdistrplus does in principle everything which I need, but if require me
>> to specify not only the density function d, but also the cumulative p and
>> and inverse cumulative function q (see for instance
>>
>> http://www.stat.umn.edu/geyer/old/5101/rlook.html
>>
>> to understand what these quantities are in the case of a normal
>> distribution).
>>
>> The analytical calculation of p and q is a big task in my case, so my
>> question is if there is a workaround for this, i.e. a way to fit the
>> unknown parameters of my probability distribution without specifying (at
>> least analytically) p and q, but only the density d.
>> Many thanks
>>
>> Lorenzo
>>
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>>
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>
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