Steffen Müller > Statistics-EfficiencyCI-0.05 > Statistics::EfficiencyCI
Module Version: 0.05   Source   Latest Release: Statistics-EfficiencyCI-0.07

# NAME

Statistics::EfficiencyCI - Robust confidence intervals on efficiencies

# SYNOPSIS

```  use Statistics::EfficiencyCI qw(efficiency_ci);
my \$confidence_level = 0.683;
my (\$mode, \$lower_cl, \$upper_cl) = efficiency_ci(\$k, \$N, \$confidence_level);

# With default confidence level of "1sigma" == 0.683
my (\$mode, \$lower_cl, \$upper_cl) = efficiency_ci(\$k, \$N);```

# DESCRIPTION

This module implements robust confidence interval calculations on efficiency-like quantities. The algorithm is explained in the note by Marc Paterno linked in the references below.

The employed method does not suffer from the usual boundary issue of the uncertainty calculation based on the Binomial model: At an efficiency `e = k/N` with small `k`, the confidence interval will be asymmetric and will not go below `0`, which the simple calculation based on the Binomial PDF will for confidence levels above the equivalent of one sigma. It also does not suffer from the problem that the uncertainty vanishes at `k=0` and `k=N`.

Beside the `efficiency_ci` function, this module exposes the approximation to the logarithm of the Gamma function that it uses internally. It takes a floating point number as argument and returns the calculated `log(Gamma(x))`. For negative integers, it returns `undef`.

## EXPORTS

This module will optionally export the `efficiency_ci` and `log_gamma` functions.

Marc Paterno's note on calculating the uncertainty on an efficiency: :<http://home.fnal.gov/~paterno/images/effic.pdf>

The ROOT library's website: http://root.cern.ch

# AUTHOR

Author of the Perl glue code is Steffen Mueller, <smueller@cpan.org>.

Author of the method of calculating the confidence intervals and its implementation is Marc Paterno.