from small samples affected by background

The problem of inferring the binomial parameter *p*
from *x* *successes* obtained in *n* *trials*
is reviewed and extended to take into account the presence
of background, that can affect
the data in two ways: *a*) fake successes are due to
a background modeled as a Poisson process of known intensity;
*b*) fake trials are due to
a background modeled as a Poisson process of known intensity,
each trial being characterized by a known
success probability *p*_{b}.

**Reference** to this paper: physics/0412069

**Printable versions and related topics** at this URL.

- Introduction
- The binomial distribution and its inverse problem
- Inferring in absence of background

- Poisson background on the observed number of
`successes'

- Poisson background on the observed number of `trials'
and of `successes'

- Conclusions
- Bibliography
- About this document ...

Giulio D'Agostini 2004-12-13