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# Ticket #8308 (closed Bugs: fixed)

## Poisson Quantile function returns wrong results in certain cases

Reported by: | Caleb.Welton@… | Owned by: | johnmaddock |
---|---|---|---|

Milestone: | To Be Determined | Component: | math |

Version: | Boost 1.52.0 | Severity: | Problem |

Keywords: | Cc: |

### Description

Sample use case:

main() { double pi = 3.1415927; boost::math::poisson poisson(pi); // std::cout << quantile(poisson, 0.00) << " "; std::cout << quantile(poisson, 0.05) << " "; std::cout << quantile(poisson, 0.30) << " "; std::cout << quantile(poisson, pi/6) << " "; std::cout << quantile(poisson, 0.7) << " "; std::cout << quantile(poisson, 1-1e-10) << " "; // std:: cout << quantile(poisson, 1) << std::endl; }

Produces the results (error), 0, 1, 3, 4, 20, (error)

Similar code in R or MATLAB results in: (0),1,2,3,4,20,(Inf)

R> qpois(c(0,0.05,0.3,pi/6,0.7,1-1e-10,1),pi) [1] 0 1 2 3 4 20 Inf MATLAB> f := stats::poissonQuantile(PI): MATLAB> f(0), f(1/20), f(0.3), f(PI/6), f(0.7), f(1-1/10^10), f(1) 0,1,2,3,4,20,Inf

The errors on the edge cases are less troubling than the seemingly incorrect results at low probabilities.

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I'll look into the edge cases (0 and 1) shortly - the differences in the other values you see are intended behaviour, given:

then the default behaviour of:

is to return the largest integer i such that

cdf(pd, i) <= 0.05, which really is the value 0, not 1 as the other programs suggest.Whether that is actually the correct thing to do depends upon the actual test you are conducting (I assume R and Mathlab calculate the quantile as a real-value and then round to the nearest int). You can configure Boost.Math to do whatever you want here, see: http://www.boost.org/doc/libs/1_53_0/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html