Re: [boost] [math distributions] Laplace distribution

Subject: Re: [boost] [math distributions] Laplace distribution
From: Thijs van den Berg (thijs_at_[hidden])
Date: 2008-11-29 04:55:39

Paul A. Bristow wrote:
>   
>> -----Original Message-----
>> From: boost-bounces_at_[hidden] [mailto:boost-bounces_at_[hidden]]
>>     
> On
>   
>> Behalf Of Thijs van den Berg
>> Sent: 28 November 2008 13:58
>> To: boost_at_[hidden]
>> Subject: Re: [boost] [math distributions] Laplace distribution
>>     
>
>   
>> I've done a first commit to the sandbox!
>>
>> 1) sandbox\math_toolkit\boost\math\distributions\laplace.cpp
>> 2) sandbox\math_toolkit\libs\math\test\test_laplace.cpp
>>
>> ..more later! (doc's, equations, charts, discussion)
>>
>>
>> The unit test file was (is) quite a lot of work, ..there are *so many*
>>     
> things to consider/check.
>
> ;-))
>  
>   
>> How about this:
>> We could write some generic test based on the properties of
>>     
> distributions...
>   
>> General relations:
>> 1) quantile(cdf(x)) == x
>> 2) hazard(x) = pdf(x)/(1-cdf(x))
>> 3) pdf(x,location,scale) = pdf( (x-location)/scale, 0, 1)/scale
>> 4) cdf(x,location,scale) = cdf( (x-location)/scale, 0, 1)
>> 5) cdf(complement(N,x)) = cdf(N(-x))
>> 6) quantile(complement(N,p)) = quantile(N(-x,1-p))
>>
>> perhaps some automatic checking (for all distribution) of error throwing
>> 7) support <-> cdf, pdf
>> 8) quantile <-> p=0, p=1
>>
>> And some generic test for distributions with specific properties Symmetric
>> distributions:
>> pdf(x) = pdf(-x)
>> cdf(x) = 1-cdf(-x)
>>
>> etc.
>> we could write template functions for that, that get passed a set of 'x'
>>     
> values etc
>
> That would indeed be neat - but our tests just grew like Topsy ;-)
>
> And it would be quite a lot of work to change now.
>
> I also worry that the acceptable tolerances vary widely, so you would have
> keep passing these as parameters anyway.
>
> We also (still are) a bit schizophrenic about whether to allow infinity as
> parameter, so a uniform test to check throw would be difficult.
>
>   
great idea. We could make an orthogonal unit test, testing all 
distributions for this specific case
> I note you haven't tried to deal with the long double case.  Even if your
> system like my MSVC only does double == long double 64 bit reals, we should
> have the hooks in place for systems that do proper long doubles.
>
> This rather messy code does this, if appropriate.
>
> #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
>   test_spots(0.0L); // Test long double.
> #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
>   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
> #endif
> #else
>    std::cout << "<note>The long double tests have been disabled on this
> platform "
>       "either because the long double overloads of the usual math functions
> are "
>       "not available at all, or because they are too inaccurate for these
> tests "
>       "to pass.</note>" << std::cout;
> #endif
>
>   
thanks! I'll include this.
> At least a few really accurate values could be calculated using the
> published formula using a 100 decimal digit calculator?
> But round tripping should test well and I don't expect any trouble for
> higher precision types (in the unlikely event that someone want them - no
> accounting for some peoples taste).
>
>   
I found it quite difficult to find reference matireal. Enough references 
to equations, but very little reference
to numerical values. The only benchmark tool I have that implements 
Laplace is GNU Octave.

I  found that Mathematica also has the Laplace distribution . Some high 
precision numerical values
generated by Mathematics would be very welcome!
> (I wonder if we can get rid of the Borland test yet?)
>
> You might also check the convenience typedef works  like this?
>
>    // Check that can generate lognormal distribution using the two
> convenience methods:
>    boost::math::lognormal myf1(1., 2); // Using typedef
>    lognormal_distribution<> myf2(1., 2); // Using default RealType double.
>
>   
Yes, those should also be checked.
> http://mathworld.wolfram.com/LaplaceDistribution.html is a good link for the
> doc?
> Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web
> Resource. http://mathworld.wolfram.com/LaplaceDistribution.html
>
> <aside>
> (This looks rather amusing
> http://demonstrations.wolfram.com/SampleVersusTheoreticalDistribution/).
> </aside>
>
> Looking good to me.
>
> Paul
>
> PS You can write 
>
> 2. 1., , 0.5, 0.25... without the L because they can be exactly represented
> as float, double, long double (unlike 0.1, 0.01... )
>
>   
nice!
> static_cast<RealType>(0.5)
>
> which saves some typing and clutter.
>
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>   

-- 
SITMO Quantitative Financial Consultancy - Software Development
M.A. (Thijs) van den Berg
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