Gregory - 8 months ago 43

Javascript Question

Javascript>

If you are in the data science industry, you would be bothered if you don't have normal distribution table. I came across the article in Stackoverflow that converts z-score to probability in JavaScript. What I really want to know is the **reverse calculation** of this function.

`/**`

* @param {number} z - Number of standard deviations from the mean.

*/

function GetZPercent(z) {

// If z is greater than 6.5 standard deviations from the mean

// the number of significant digits will be outside of a reasonable

// range.

if (z < -6.5)

return 0.0;

if (z > 6.5)

return 1.0;

var factK = 1;

var sum = 0;

var term = 1;

var k = 0;

var loopStop = Math.exp(-23);

while (Math.abs(term) > loopStop) {

term = 0.3989422804 * Math.pow(-1, k) * Math.pow(z, k) / (2 * k + 1) /

Math.pow(2, k) * Math.pow(z, k + 1) / factK;

sum += term;

k++;

factK *= k;

}

sum += 0.5;

return sum;

}

I have a sense of how to convert z-score into the probability. But, I have no idea how to calculate the z-score(Standard deviation) from corresponding probability in javascript. For example, If I put in 0.95 (or 95%), I can expect to get 2.25 standard deviation. Above code gives me 95%, if I enter 2.25.

Answer

Here is a function that does an opposite calculation (probability to z-score):

```
function percentile_z(p) {
var a0= 2.5066282, a1=-18.6150006, a2= 41.3911977, a3=-25.4410605,
b1=-8.4735109, b2= 23.0833674, b3=-21.0622410, b4= 3.1308291,
c0=-2.7871893, c1= -2.2979648, c2= 4.8501413, c3= 2.3212128,
d1= 3.5438892, d2= 1.6370678, r, z;
if (p>0.42) {
r=Math.sqrt(-Math.log(0.5-p));
z=(((c3*r+c2)*r+c1)*r+c0)/((d2*r+d1)*r+1);
} else {
r=p*p;
z=p*(((a3*r+a2)*r+a1)*r+a0)/((((b4*r+b3)*r+b2)*r+b1)*r+1);
}
return z;
}
```

Grabbed from easycalculation.com