# NAME

Statistics::PointEstimation - Perl module for computing confidence intervals in parameter estimation with Student's T distribution Statistics::PointEstimation::Sufficient - Perl module for computing the confidence intervals using sufficient statistics

# SYNOPSIS

``````  # example for Statistics::PointEstimation
use Statistics::PointEstimation;

my @r=();
for(\$i=1;\$i<=32;\$i++) #generate a uniformly distributed sample with mean=5
{

\$rand=rand(10);
push @r,\$rand;
}

my \$stat = new Statistics::PointEstimation;
\$stat->set_significance(95); #set the significance(confidence) level to 95%
\$stat->output_confidence_interval(); #output summary
\$stat->print_confidence_interval();  #output the data hash related to confidence interval estimation

#the following is the same as \$stat->output_confidence_interval();
print "Summary  from the observed values of the sample:\n";
print "\tsample size= ", \$stat->count()," , degree of freedom=", \$stat->df(), "\n";
print "\tmean=", \$stat->mean()," , variance=", \$stat->variance(),"\n";
print "\tstandard deviation=", \$stat->standard_deviation()," , standard error=", \$stat->standard_error(),"\n";
print "\t the estimate of the mean is ", \$stat->mean()," +/- ",\$stat->delta(),"\n\t",
" or (",\$stat->lower_clm()," to ",\$stat->upper_clm," ) with ",\$stat->significance," % of confidence\n";
print "\t t-statistic=T=",\$stat->t_statistic()," , Prob >|T|=",\$stat->t_prob(),"\n";

#example for Statistics::PointEstimation::Sufficient

use strict;
use Statistics::PointEstimation;
my (\$count,\$mean,\$variance)=(30,3.996,1.235);
my \$stat = new Statistics::PointEstimation::Sufficient;
\$stat->set_significance(99);
\$stat->output_confidence_interval();
\$stat->set_significance(95);
\$stat->output_confidence_interval();``````

# DESCRIPTION

## Statistics::PointEstimation

``````  This module is a subclass of Statistics::Descriptive::Full. It uses T-distribution for point estimation
assuming the data is normally distributed or the sample size is sufficiently large. It overrides the
add_data() method in Statistics::Descriptive to compute the confidence interval with the specified significance
level (default is 95%). It also computes the t-statistic=T and Prob>|T| in case of hypothesis
testing of paired T-tests.``````

## Statistics::PointEstimation::Sufficient

`````` This module is a subclass of Statistics::PointEstimation. Instead of taking the real data points as the input,
it will compute the confidence intervals based on the sufficient statistics and the sample size inputted.
To use this module, you need to pass the sample size, the sample mean , and the sample variance into the load_data()
function. The output will be exactly the same as the Statistics::PointEstimation Module.
``````

# AUTHOR

Yun-Fang Juan , Yahoo! Inc. (yunfang@yahoo-inc.com)