use Math::Cephes qw(gamma incbet);
	
# スチューデントのt分布 Student's T-Distribution
# 引数 変数 自由度 ($X, $DegreesOfDreedom)
# 戻り値 スチューデントのt分布 (@StudentsTDistribution)
sub STUDENTSTDISTRIBUTION{
	my ($X, $DegreesOfDreedom) = @_;
	my @StudentsTDistribution = ();
	my $IncompleteBetaFunction = 0;
	my $t = 0;
	
	# 変数,自由度の確認
	if(($X < 0) || ($DegreesOfDreedom <= 0)){
		return 0;
	}
	
	# 確率密度関数 Frequency Function
	$StudentsTDistribution[0] = &FREQUENCYFUNCTION($X, $DegreesOfDreedom);
	
	$t = ($X + sqrt(($X * $X) + $DegreesOfDreedom)) / (2 * sqrt(($X * $X) + $DegreesOfDreedom));
	# 累積分布関数 正則不完全ベータ関数 Regularized Incomplete Beta Function
	$IncompleteBetaFunction = &incbet(($DegreesOfDreedom / 2), ($DegreesOfDreedom / 2), $t);
	
	# 下側累積確率 Lower Cumulative Distribution
	$StudentsTDistribution[1] = $IncompleteBetaFunction;
	# 上側累積確率 Upper Cumulative Distribution
	$StudentsTDistribution[2] = 1 - $IncompleteBetaFunction;
	
	return @StudentsTDistribution;
}
	
# 確率密度関数 Frequency Function
# 引数 変数 自由度 ($X, $DegreesOfDreedom)
# 戻り値 確率密度関数 ($FrequencyFunction)
sub FREQUENCYFUNCTION{
	my ($X, $DegreesOfDreedom) = @_;
	my $FrequencyFunction = 0;
	my $Pi = atan2(1, 1) * 4;
	my $Num = 0;
	my $Den = 0;
	
	# 分子
	$Num = gamma(($DegreesOfDreedom + 1) / 2);
	# 分母
	$Den = sqrt($DegreesOfDreedom * $Pi) * gamma($DegreesOfDreedom / 2);
	# スチューデントのt分布 Frequency Function
	$FrequencyFunction = ($Num / $Den) * ((1 + (($X * $X) / $DegreesOfDreedom)) ** (-(($DegreesOfDreedom + 1) / 2)));
	
	return $FrequencyFunction;
}