[math/distributions] invalid values for undefined moments
Hi, According to the documentation, in boost 1-50 non-member functions of moments (e.g. mean, variance) which are not defined for a given distribution shall issue compile-time errors, or throw a domain_error at runtime otherwise. For the Cauchy Distribution, that's what it does. For the t-distribution, that's not what it does - the non-member functions happily return some complete rubbish values for mean and variance (and hence I'd also suppose standard deviation). For kurtosis and skewness it seems to work correctly but are subject to mathematical definitions. I have not tested other non-member functions. Note that there are different definitions floating around as to when a given moment is defined. The k-th moment is always defined if k < v, but in other cases opinions deviate. Wikipedia states it might be infinity under some circumstances - obviously what boost seems to having taken over. In general however I am used to - and my gut feeling the clear majority of people would have this perception; indeed I am not aware of any other source than wikipedia stating these infinity things - that moments are undefined if k >= v (see e.g. Probability and Statistics, DeGroot & Schervish 2002, for a professional textbooks and heaps of other sources). So while the boost output for variance and a t-2 distribution (or alternatively also the kurtosis of a t-4 distribution) might be considered ok by some, I'd guess to most people it would be fairly unexpected? It had been a surprise to me, at least. Code snippet: typedef boost::math::students_t_distribution<double> t_distr; // this is ok std::cout << "mean(t(2)): " << boost::math::mean( t_distr(2) ) << std::endl; // this is NOT ok - first moment not defined for given distribution std::cout << "mean(t(1)): " << boost::math::mean( t_distr(1) ) << std::endl; // this is ok std::cout << "var(t(3)): " << boost::math::variance( t_distr(3) ) << std::endl; // this might be ok or not // depending on point of view, either Inf or undefined std::cout << "var(t(2)): " << boost::math::variance( t_distr(2) ) << std::endl; // this is NOT ok - second moment not defined for the given distribution std::cout << "var(t(1)): " << boost::math::variance( t_distr(1) ) << std::endl; best, Thomas
-----Original Message----- From: boost-users-bounces@lists.boost.org [mailto:boost-users-bounces@lists.boost.org] On Behalf Of Thomas Mang Sent: Thursday, July 26, 2012 12:52 AM To: boost-users@lists.boost.org Subject: [Boost-users] [math/distributions] invalid values for undefined moments
Hi,
According to the documentation, in boost 1-50 non-member functions of moments (e.g. mean, variance) which are not defined for a given distribution shall issue compile-time errors, or throw a domain_error at runtime otherwise. For the Cauchy Distribution, that's what it does. For the t-distribution, that's not what it does - the non-member functions happily return some complete rubbish values for mean and variance (and hence I'd also suppose standard deviation). For kurtosis and skewness it seems to work correctly but are subject to mathematical definitions. I have not tested other non-member functions.
Note that there are different definitions floating around as to when a given moment is defined. The k-th moment is always defined if k < v, but in other cases opinions deviate. Wikipedia states it might be infinity under some circumstances - obviously what boost seems to having taken over. In general however I am used to - and my gut feeling the clear majority of people would have this perception; indeed I am not aware of any other source than wikipedia stating these infinity things - that moments are undefined if k >= v (see e.g. Probability and Statistics, DeGroot & Schervish 2002, for a professional textbooks and heaps of other sources). So while the boost output for variance and a t-2 distribution (or alternatively also the kurtosis of a t-4 distribution) might be considered ok by some, I'd guess to most people it would be fairly unexpected? It had been a surprise to me, at least.
Code snippet:
typedef boost::math::students_t_distribution<double> t_distr;
// this is ok std::cout << "mean(t(2)): " << boost::math::mean( t_distr(2) ) << std::endl;
// this is NOT ok - first moment not defined for given distribution std::cout << "mean(t(1)): " << boost::math::mean( t_distr(1) ) << std::endl;
// this is ok std::cout << "var(t(3)): " << boost::math::variance( t_distr(3) ) << std::endl;
// this might be ok or not // depending on point of view, either Inf or undefined std::cout << "var(t(2)): " << boost::math::variance( t_distr(2) ) << std::endl;
// this is NOT ok - second moment not defined for the given distribution std::cout << "var(t(1)): " << boost::math::variance( t_distr(1) ) << std::endl;
Looks like a buglet and will investigate soon. https://svn.boost.org/trac/boost/ticket/7177 Paul
participants (2)
-
Paul A. Bristow -
Thomas Mang