Question

我需要在MySQL中使用逆正态累积分布函数（在Excel中是NORMSINV函数），但是那里没有这样的函数。也许你们中有人为MySQL实现了它？

非常感谢你的时间。

Answer 1

好吧，我终于找到了这个。这不是完美的，而是非常好的近似。代码不是我的，其作者是Geoffrey C. Barnes。我刚刚将它从VB.NET转换为MySQL。

DROP FUNCTION IF EXISTS NORMSINV;
DELIMITER //

CREATE FUNCTION NORMSINV (p DOUBLE) RETURNS DOUBLE
BEGIN

DECLARE q, r DOUBLE;
DECLARE A1, A2, A3, A4, A5, A6 DOUBLE;
DECLARE B1, B2, B3, B4, B5 DOUBLE;
DECLARE C1, C2, C3, C4, C5, C6 DOUBLE;
DECLARE D1, D2, D3, D4 DOUBLE;
DECLARE P_LOW, P_HIGH DOUBLE;

/* coefficients in rational approximations */
SET A1 = -39.696830286653757;
SET A2 = 220.9460984245205;
SET A3 = -275.92851044696869;
SET A4 = 138.357751867269;
SET A5 = -30.66479806614716;
SET A6 = 2.5066282774592392;

SET B1 = -54.476098798224058;
SET B2 = 161.58583685804089;
SET B3 = -155.69897985988661;
SET B4 = 66.80131188771972;
SET B5 = -13.280681552885721;

SET C1 = -0.0077848940024302926;
SET C2 = -0.32239645804113648;
SET C3 = -2.4007582771618381;
SET C4 = -2.5497325393437338;
SET C5 = 4.3746641414649678;
SET C6 = 2.9381639826987831;

SET D1 = 0.0077846957090414622;
SET D2 = 0.32246712907003983;
SET D3 = 2.445134137142996;
SET D4 = 3.7544086619074162;

/* define break points */
SET P_LOW = 0.02425;
SET P_HIGH = 1 - P_LOW;

IF (p > 0 AND p < P_LOW) THEN
/* rational approximation for lower region */
SET q = SQRT(-2 * LOG(p));
RETURN (((((C1 * q + C2) * q + C3) * q + C4) * q + C5) * q + C6) /  
       ((((D1 * q + D2) * q + D3) * q + D4) * q + 1);

ELSEIF (p >= P_LOW AND p <= P_HIGH) THEN
/* rational approximation for central region */
SET q = p - 0.5;
SET r = q * q;
RETURN (((((A1 * r + A2) * r + A3) * r + A4) * r + A5) * r + A6) * q / 
       (((((B1 * r + B2) * r + B3) * r + B4) * r + B5) * r + 1);

ELSEIF (p > P_HIGH AND p < 1) THEN
/* rational approximation for upper region */
SET q = SQRT(-2 * LOG(1 - p));
RETURN -(((((C1 * q + C2) * q + C3) * q + C4) * q + C5) * q + C6) / 
       ((((D1 * q + D2) * q + D3) * q + D4) * q + 1);

/* on error returning 0 */           
ELSE
RETURN 0;
END IF;

END//
DELIMITER ;

Answer 2

下面是Excel的NORMINV函数的等效项。

CREATE FUNCTION NORMINV(p double, mu double, sigma double)
RETURNS decimal(20,6)
begin
    declare q   double;
    declare r   double;
    declare val double;
BEGIN
    IF p < 0 OR p > 1 THEN
        signal sqlstate '20100' set message_text= 'The probality p must be bigger than 0 and smaller than 1';
    END IF;
    IF sigma < 0 THEN
        signal sqlstate '20100' set message_text=  'The standard deviation sigma must be positive';
    END IF;
    IF p = 0 THEN 
        RETURN to_binary_double('-INF');    
    END IF;
    IF p = 1 THEN
        RETURN to_binary_double('INF');
    END IF;
    IF sigma = 0 THEN
        RETURN mu;
    END IF;

    set q:= p - 0.5;

    IF(ABS(q) <= .425) THEN
            set r:= .180625 - q * q;
            set val :=
                 q * (((((((r * 2509.0809287301226727 +
                            33430.575583588128105) * r + 67265.770927008700853) * r +
                          45921.953931549871457) * r + 13731.693765509461125) * r +
                        1971.5909503065514427) * r + 133.14166789178437745) * r +
                      3.387132872796366608)
                 / (((((((r * 5226.495278852854561 +
                          28729.085735721942674) * r + 39307.89580009271061) * r +
                        21213.794301586595867) * r + 5394.1960214247511077) * r +
                      687.1870074920579083) * r + 42.313330701600911252) * r + 1);
    ELSE
        /* r = min(p, 1-p) < 0.075 */
        IF q > 0 THEN
            set r:= 1 - p;
        ELSE
            set r:= p;
        END IF;

        set r:= SQRT(-LN(r));
        /* r = sqrt(-log(r))  <==>  min(p, 1-p) = exp( - r^2 ) */

        IF (r <= 5) THEN
            set r:= r - 1.6;
            set val := (((((((r * 7.7454501427834140764e-4 +
                         .0227238449892691845833) * r + .24178072517745061177) *
                       r + 1.27045825245236838258) * r +
                      3.64784832476320460504) * r + 5.7694972214606914055) *
                    r + 4.6303378461565452959) * r +
                   1.42343711074968357734)
                  / (((((((r *
                           1.05075007164441684324e-9 + 5.475938084995344946e-4) *
                          r + .0151986665636164571966) * r +
                         .14810397642748007459) * r + .68976733498510000455) *
                       r + 1.6763848301838038494) * r +
                      2.05319162663775882187) * r + 1);
        ELSE /* very close to  0 or 1 */
            set r := r - 5;
            set val := (((((((r * 2.01033439929228813265e-7 +
                         2.71155556874348757815e-5) * r +
                        .0012426609473880784386) * r + .026532189526576123093) *
                      r + .29656057182850489123) * r +
                     1.7848265399172913358) * r + 5.4637849111641143699) *
                   r + 6.6579046435011037772)
                  / (((((((r *
                           2.04426310338993978564e-15 + 1.4215117583164458887e-7) *
                          r + 1.8463183175100546818e-5) * r +
                         7.868691311456132591e-4) * r + .0148753612908506148525)
                       * r + .13692988092273580531) * r +
                      .59983220655588793769) * r + 1);
        END IF;

        IF q < 0.0 THEN
            set val := -val;
        END IF;
    END IF;

    RETURN mu + sigma * val;
END;
END

它已从[https://forums.mysql.com/read.php?98,411441,411458#msg-411458]（它是Oracle等效文件）改编而来。用过了，到目前为止还不错。希望能对某人有所帮助。

在MySQL中实现NORMSINV函数

2 个答案: