Statistics::PointEstimation - Perl module for computing confidence intervals in parameter estimation with Student's T distribution

  # 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->add_data(@r);
  $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);
  $stat->load_data($count,$mean,$variance);
  $stat->output_confidence_interval();
  $stat->set_significance(95);
  $stat->output_confidence_interval();

  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.

 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.

package Statistics::PointEstimation;
use strict;
use Carp;
use vars qw($VERSION @ISA $AUTOLOAD);
use Statistics::Distributions qw(chisqrdistr tdistr fdistr udistr uprob chisqrprob tprob fprob);
use Statistics::Descriptive;
use POSIX;


@ISA= qw (Statistics::Descriptive::Full);
$VERSION = '1.1';
my %confidence_interval=  #data related to confidence interval 
(

	"significance" => undef,
	"alpha" => undef,
	"df" =>undef,
	"standard_error" => undef,
	"t_value" =>undef, 
	"t_statistic" =>undef,
	"t_prob" =>undef,
	"delta" =>undef,
	"upper_clm" => undef,
	"lower_clm" =>undef,
	"valid"  =>undef
);


	
sub new{
	my $proto = shift;
	my $class = ref($proto) || $proto;
	my $self = $class->SUPER::new();  
	my %confidence=%confidence_interval;
	$self->{confidence}=\%confidence;
	bless ($self, $class);  
	return $self;
}

sub compute_confidence_interval{
	my $self=shift;
	croak "sample size must be >1 to compute the confidence interval \n" if($self->count()<=1);
	$self->{'significance'}=95 if (!defined($self->{'significance'}));
	$self->{df}=$self->count()-1;
	$self->{alpha}=(100-$self->{significance})/2;
	$self->{alpha}/=100;
	$self->{standard_error}=$self->standard_deviation()/sqrt($self->count());
	$self->{t_value}=abs tdistr($self->{df},$self->{alpha});
	$self->{delta}=$self->{t_value}*$self->{standard_error};

	$self->{upper_clm}=$self->mean() +$self->{delta};
	$self->{lower_clm}=$self->mean() -$self->{delta};
	$self->{t_statistic}=$self->{standard_error}
						?($self->mean()/$self->{standard_error}):0;
	$self->{t_prob}=1- abs (tprob($self->{df},-1*$self->{t_statistic})-tprob($self->{df},$self->{t_statistic})) ;
	$self->{valid}=1;
	return 1;

}
sub add_data{
	my $self = shift;
	my $aref;

	if (ref $_[0] eq 'ARRAY') {
		$aref = $_[0];
	}
	else {
		$aref = \@_;
	}
	my $significance=$self->{'significance'} if (defined($self->{'significance'}));
	$self->SUPER::add_data($aref);
	$self->{'significance'}=$significance;
	$self->compute_confidence_interval() if ((defined($self->{count}))&&($self->{count}>1)) ;

	return 1;

}
sub set_significance{   # set the significance level. usually 90, 95 or 99 
	my $self=shift;
	my $significance=shift;
	$self->{'significance'}=$significance if (($significance>0)&&($significance<100));
	$self->compute_confidence_interval() if((defined($self->{count}))&&($self->{count}>1));
	return 1;

}

sub print_confidence_interval{
	my $self=shift;
	print "mean:",$self->mean(),"\n";
	print "variance:",$self->variance(),"\n";
	my $confidence=\%confidence_interval;

	foreach my $k ( keys %$confidence)
	{
		print "$k:", $self->{$k}," \n";
	}
	return 1;

}

sub output_confidence_interval{
	my $self=shift;
	croak "sample size must be >1 to compute the confidence interval\n" if($self->{valid}!=1);
	my $title=shift;
	print "Summary  from the observed values of the sample $title:\n";
	print "\tsample size= ", $self->count()," , degree of freedom=", $self->df(), "\n";
	print "\tmean=", $self->mean()," , variance=", $self->variance(),"\n";
	print "\tstandard deviation=", $self->standard_deviation()," , standard error=", $self->standard_error(),"\n";
	print "\t the estimate of the mean is ", $self->mean()," +/- ",$self->delta(),"\n\t",
		" or (",$self->lower_clm()," to ",$self->upper_clm," ) with ",$self->significance," % of confidence\n"; 
	print "\t t-statistic=T=",$self->t_statistic()," , Prob >|T|=",$self->t_prob(),"\n";
}

sub AUTOLOAD{
	my $self = shift;
	my $type = ref($self)
	or croak "$self is not an object";
	my $name = $AUTOLOAD;
	$self->{_confidence}=\%confidence_interval;
	$name =~ s/.*://;     
	return if $name eq "DESTROY";
	if (exists $self->{_permitted}->{$name} ) {
		return $self->{$name};
	}
	elsif(exists $self->{'_confidence'}->{$name})
	{
		return $self->{$name};
	}
	else
	{
		croak "Can't access `$name' field in class $type";
	}
}
1;

package Statistics::PointEstimation::Sufficient;
use strict;
use Carp;
use vars qw($VERSION $AUTOLOAD @ISA);
use POSIX;
@ISA=qw (Statistics::PointEstimation);
$VERSION='1.1';
my %fields=  #data related to confidence interval 
(
        "count"=>undef, 
        "mean" =>undef,
        "variance" => undef,
        "standard_deviation" =>undef,
        "significance" => undef,
        "alpha" => undef,
        "df" =>undef,
        "standard_error" => undef,
        "t_value" =>undef, 
        "t_statistic" =>undef,
        "t_prob" =>undef,
        "delta" =>undef,
        "upper_clm" => undef,
        "lower_clm" =>undef,
        "valid"  =>undef
);

sub new{
        my $proto = shift;
        my $class = ref($proto) || $proto;
        my $self = {%fields};  
        bless ($self, $class);  
        return $self;
}
sub add_data{

     croak "the add_data() method is not supported in Statistics::PointEstimation::Sufficient\n";

}
sub load_data{
        my $self=shift;
        my ($count,$mean,$variance)=@_;
        $self->{count}=$count;
        $self->{mean}=$mean;
        $self->{variance}=$variance;
        $self->{standard_deviation}=sqrt($variance);
        $self->compute_confidence_interval() if ($self->count()>1) ;
        return;

}

sub AUTOLOAD{
        my $self = shift;
        my $type = ref($self)
        or croak "$self is not an object";
        $self->{_confidence}=\%fields;
        my $name = $AUTOLOAD;
        $name =~ s/.*://;     
        return if $name eq "DESTROY";

        if(exists $self->{_confidence}->{$name})
        {
                return $self->{$name};
        }
        else
        {
                croak "Can't access `$name' field in class $type";
        }
}
1;
 

__END__