# [R-SIG-Mac] rnorm.halton

Christophe Dutang dutangc at gmail.com
Tue Sep 15 18:36:07 CEST 2009

```Ok so you mistype pseudo instead of quasi. My Email was useless... I
will get snow Leopard in the coming days and will try to reproduce
your problem. Did you compile R 64 yourself?

iPhone.fan

Le 15 sept. 2009 à 18:25, Anirban Mukherjee <anirbanm at smu.edu.sg> a
écrit :

> Sorry, what I should have said was Halton numbers are quasi-random,
> and not pseudo-random. Quasi-random is the technically appropriate
> terminology.
>
> Halton sequences are low discrepancy: the subsequence looks/smells
> random. Hence, they are often used in quasi monte carlo simulations.
> To be precise, there is only 1 Halton sequence for a particular prime.
> Repeated calls to Halton should return the same numbers. The first
> column is the Halton sequence for 2. the second for 3, the third for 5
> and so on using the first M primes (for M columns). (You can also
> scramble the sequence to avoid this.)
>
> I am using them to integrate over a multivariate normal space. If you
> take 1000 random draws, then sum f() over the draws is the expectation
> of f(). If f() is very non-linear (and/or multi-variate) then even
> with large N, its often hard to get a good integral. With quasi-random
> draws, the integration is better for the same N. (One uses the inverse
> distribution function.) For an example, you can look at Train's paper
> (page 4 and 5 have a good explanation) at:
>
> http://elsa.berkeley.edu/wp/train0899.pdf
>
> In the context of simulated maximum likelihood estimation, such
> integrals are very common. Of course true randomness has its own
> place/importance: its just that quasi-random numbers can be very
> useful in certain contexts.
>
> Regards,
> Anirban
>
> PS: qnorm(halton()) gets around the problem of the random deviates
> not working.
>
> On Tue, Sep 15, 2009 at 11:37 AM, David Winsemius
> <dwinsemius at comcast.net> wrote:
>>
>> On Sep 15, 2009, at 11:10 AM, Anirban Mukherjee wrote:
>>
>>> Thanks everyone for your replies. Particularly David.
>>>
>>> The numbers are pseudo-random. Repeated calls should/would give the
>>> same output.
>>
>> As I said, this package is not one with which I have experience. It
>> has _not_ however the case that repeated calls to (typical?) random
>> number functions give the same output when called repeatedly:
>>
>>  > rnorm(10)
>>   [1] -0.8740195  2.1827411 -0.1473012 -1.4406262  0.1820631
>> -1.3151244 -0.4813703  0.8177692
>>   [9]  0.2076117  1.8697418
>>  > rnorm(10)
>>   [1] -0.7725731  0.8696742 -0.4907099  0.1561859  0.5913528
>> -0.8441891  0.2285653 -0.1231755
>>   [9]  0.5190459 -0.7803617
>>  > rnorm(10)
>>   [1] -0.9585881 -0.0458582  1.1967342  0.6421980 -0.5290280
>> -1.0735112  0.6346301  0.2685760
>>   [9]  1.5767800  1.0864515
>>  > rnorm(10)
>>   [1] -0.60400852 -0.06611533  1.00787048  1.48289305  0.54658888
>> -0.67630052  0.52664127 -0.36449997
>>   [9]  0.88039397  0.56929333
>>
>> I cannot imagine a situation where one would _want_ the output to be
>> the same on repeated calls unless one reset a seed. Unless perhaps I
>> am not understanding the meaning of "random" in the financial domain?
>>
>> --
>> David
>>
>>>   Currently, Halton works fine when used to just get the
>>> Halton sequence, but the random deviates call is not working in 64
>>> bit
>>> R. For now, I will generate the numbers in 32 bit R, save them and
>>> then load them back in when using 64 bit R. The package maintainers
>>> can look at it if/when they get a chance and/or access to 64 bit R.
>>>
>>> Thanks!
>>>
>>> Best,
>>> Anirban
>>>
>>> On Tue, Sep 15, 2009 at 9:01 AM, David Winsemius <dwinsemius at comcast.net
>>>> wrote:
>>>> I get very different output from the two versions of Mac OSX R as
>>>> well. The 32 bit version puts out a histogram that has an expected,
>>>> almost symmetric unimodal distribution. The 64 bit version
>>>> created a
>>>> bimodal distribution with one large mode near 0 and another smaller
>>>> mode near 10E+37. Postcript output attached.
>>>>
>>>
>>>
>>>
>>> --
>>> Anirban Mukherjee | Assistant Professor, Marketing | LKCSB, SMU
>>> +65-6828-1932
>>>
>>> _______________________________________________
>>> R-SIG-Mac mailing list
>>> R-SIG-Mac at stat.math.ethz.ch
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mac
>>
>> David Winsemius, MD
>> Heritage Laboratories
>> West Hartford, CT
>>
>>
>
>
>
> --
> Anirban Mukherjee | Assistant Professor, Marketing | LKCSB, SMU
> 5062 School of Business, 50 Stamford Road, Singapore 178899 | +65-6828-1932
>
> _______________________________________________
> R-SIG-Mac mailing list
> R-SIG-Mac at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/r-sig-mac

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