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**Section:** 26.6.9.5.3 [rand.dist.norm.chisq] **Status:** CD1
**Submitter:** Stephan Tolksdorf **Opened:** 2007-09-21 **Last modified:** 2016-02-10

**Priority: **Not Prioritized

**View all issues with** CD1 status.

**Discussion:**

`chi_squared_distribution`, `fisher_f_distribution` and `student_t_distribution`
have parameters for the "degrees of freedom" `n` and `m` that are specified as integers. For the
following two reasons this is an unnecessary restriction: First, in many applications such as
Bayesian inference or Monte Carlo simulations it is more convenient to treat the respective param-
eters as continuous variables. Second, the standard non-naive algorithms (i.e.
O(1) algorithms) for simulating from these distributions work with floating-point parameters anyway (all
three distributions could be easily implemented using the Gamma distribution, for instance).

Similar arguments could in principle be made for the parameters `t` and `k` of the discrete
`binomial_distribution` and `negative_binomial_distribution`, though in both cases continuous
parameters are less frequently used in practice and in case of the `binomial_distribution`
the implementation would be significantly complicated by a non-discrete parameter (in most
implementations one would need an approximation of the log-gamma function instead of just the
log-factorial function).

**Possible resolution:** For these reasons, I propose to change the type of the respective parameters
to double.

*[
Bellevue:
]*

In N2424. Not wildly enthusiastic, not really felt necessary. Less frequently used in practice. Not terribly bad either. Move to OPEN.

*[
Sophia Antipolis:
]*

Marc Paterno: The generalizations were explicitly left out when designing the facility. It's harder to test.

Marc Paterno: Ask implementers whether floating-point is a significant burden.

Alisdair: It's neater to do it now, do ask Bill Plauger.

Disposition: move to review with the option for "NAD" if it's not straightforward to implement; unanimous consent.

**Proposed resolution:**

See N2424 for the proposed resolution.

*[
Stephan Tolksdorf adds pre-Bellevue:
]*

In 26.6.9.5.3 [rand.dist.norm.chisq]:

Delete ", where

nis a positive integer" in the first paragraph.Replace both occurrences of "

explicit chi_squared_distribution(int n = 1);" with "explicit chi_squared_distribution(RealType n = 1);".Replace both occurrences of "

int n() const;" with "RealType n() const;".In 26.6.9.5.5 [rand.dist.norm.f]:

Delete ", where

mandnare positive integers" in the first paragraph.Replace both occurrences of

explicit fisher_f_distribution(int m = 1, int n = 1);with

explicit fisher_f_distribution(RealType m = 1, RealType n = 1);Replace both occurrences of "

int m() const;" with "RealType m() const;".Replace both occurrences of "

int n() const;" with "RealType n() const;".In 26.6.9.5.6 [rand.dist.norm.t]:

Delete ", where

nis a positive integer" in the first paragraph.Replace both occurrences of "

explicit student_t_distribution(int n = 1);" with "explicit student_t_distribution(RealType n = 1);".Replace both occurrences of "

int n() const;" with "RealType n() const;".