Re: [Help-gsl] Random numbers within some ranges in the domain using different distributipons?

[Martin Jansche]

On Wed, Jun 18, 2008 at 13:36, Martin Jansche <address@hidden> wrote:
> On Tue, Jun 17, 2008 at 12:44, Mohammad Khaleghi <address@hidden> wrote:
>> Hello Dan,
>>
>> Thank you very much for the email and the explaination which is very useful. 
>> I might have still some problems. It is maybe due to lack of enough 
>> knowledge in statistics :-)
>> I saw that most of the functions return double. Do you mean all these are 
>> distributed between (0, 1)? Then your solution is in these case perfect. But 
>> what should I do in the cases where a long int is returned?
>> I copied and pasted an example from the documents, where an unsined int is 
>> generated. Almost the same goes for all uniform distributions.
>>
>>
>>  Function: unsigned int gsl_ran_poisson (const gsl_rng * r, double mu)
>> This function returns a random integer from the Poisson distribution with 
>> mean mu. The probability distribution for Poisson variates is,
>> p(k) = {\mu^k \over k!} \exp(-\mu)
>> for k >= 0.
>>
>> Does the above means that the function produces long int values between (0, 
>> +inf)?
>
> Not +inf, since you cannot represent that in C's integral types; more
> likely UINT_MAX.
>
>> If so how can I produce (or get) say long ints between (100, 200)?
>
> So you want to sample from the truncated Poisson distribution.  A
> simple and correct way is the naive rejection method:
>
>  do {
>    k = gsl_ran_poisson(rng, mu);
>  } while (100 <= k && k <= 200);

And of course you need to negate that condition....
Silly me.

-- mj

> Its efficiency, however, will depend on the value of mu.  If mu << 100
> or mu >> 200, rejection sampling is going to be very inefficient.
>
> Depending on which distribution you want to sample from, there may be
> solutions in GSL already.  For example, there are routines for
> sampling from the tail of a Gaussian.
>
> What's the high-level goal you're trying to accomplish?
>
> -- mj
>
>> Does it make sense even thinking of something between (-100, 150)?
>>
>> Thanks a lot
>> Mohd
>>
>>> -----Ursprüngliche Nachricht-----
>>> Von: "Daniel J Farrell" <address@hidden>
>>> Gesendet: 17.06.08 18:01:50
>>> An: Mohammad Khaleghi <address@hidden>
>>> CC: address@hidden
>>> Betreff: Re: [Help-gsl] Random numbers within some ranges in the domain 
>>> using different distributipons?
>>
>>
>>> Hello Mohd,
>>>
>>> I think you are looking for this function:
>>>
>>> f(r) = a + (b - a) * r
>>>
>>> where a is the min value, b is the max values and r is a random number
>>> distributed between 0 and 1 (e.g. use gsl_rng_uniform_pos() to
>>> generate r).
>>>
>>> This come up a lot on the mailing list maybe it should be added to the
>>> library?
>>>
>>> Cheers,
>>>
>>> Dan.
>>>
>>>
>>>
>>> On 17 Jun 2008, at 16:26, Mohammad Khaleghi wrote:
>>>
>>> > Hi everybody!
>>> >
>>> > Could somebody please tell me how to generate random numbers within
>>> > some ranges in the domain?
>>> > I saw the documentation and did not see anything like setting a min
>>> > and max. I mean for a distribution that has a domain (-inf, + inf)
>>> > could one set some range (min, max) to sample from? Or it is not
>>> > possible with gsl?
>>> >
>>> > thans, Mohd
>>> >
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>>> >
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>>>
>>>
>>
>>
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