use Math::Cephes qw(gamma igamc);
	
# カイ二乗分布 Chi-Squared Distribution
# 引数 変数 自由度 ($X, $DegreesOfFreedom)
# 戻り値 カイ二乗分布 (@ChiSquaredDistribution)
sub CHISQUAREDDISTRIBUTION{
	my ($X, $DegreesOfFreedom) = @_;
	my @ChiSquaredDistribution = ();
	my $IncompleteGammaFunction = 0;
	
	# 変数,自由度の確認
	if(($X < 0) || ($DegreesOfFreedom <= 0)){
		return 0;
	}
	
	# 確率密度関数 Frequency Function
	$ChiSquaredDistribution[0] = &FREQUENCYFUNCTION($X, $DegreesOfFreedom);
	
	# 累積分布関数 不完全ガンマ関数 Incomplete Gamma Function
	$IncompleteGammaFunction = igamc(($DegreesOfFreedom / 2), ($X / 2));
	
	# 下側累積確率 Lower Cumulative Distribution
	$ChiSquaredDistribution[1] = 1 - $IncompleteGammaFunction;
	# 上側累積確率 Upper Cumulative Distribution
	$ChiSquaredDistribution[2] = $IncompleteGammaFunction;
	
	return @ChiSquaredDistribution;
}
	
# 確率密度関数 Frequency Function
# 引数 変数 自由度 ($X, $DegreesOfFreedom)
# 戻り値 確率密度関数 ($FrequencyFunction)
sub FREQUENCYFUNCTION{
	my ($X, $DegreesOfFreedom) = @_;
	my $FrequencyFunction = 0;
	my $Pi = atan2(1, 1) * 4;
	my $Num = 0;
	my $Den = 0;
	
	if($X == 0){
		return 0;
	}
	
	# 分子
	$Num = ($X ** (($DegreesOfFreedom / 2) - 1)) * exp(-($X / 2));
	# 分母
	$Den = (2 ** ($DegreesOfFreedom / 2)) * gamma($DegreesOfFreedom / 2);
	# カイ二乗分布 Frequency Function
	$FrequencyFunction = $Num / $Den;
	
	return $FrequencyFunction;
}