NORM.DIST on PostgreSQL

normal_dist.sql

CREATE FUNCTION norm_dist(x real, mean real, stddev real, cumulative boolean) RETURNS real AS $$
DECLARE p real;
        BEGIN
        	IF cumulative = false THEN
                SELECT (1 / (stddev * sqrt(2 * pi()))) * exp(-1 * power(x - mean, 2) / (2 * power(stddev, 2))) INTO p;
            ELSE
            	SELECT 0.5 * (1 + erf((x - mean) / (stddev * sqrt(2)))) INTO p;
            END IF;
                
            RETURN p;
        END;
$$ LANGUAGE plpgsql;

select 1.0-norm_dist(6.0,5.0,1.0,false); -- x在6.0附近的密度(作圖是高度)
select norm_dist(6.0,5.0,1.0,true); -- x<6.0的機率