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Calculate standard normal table #108

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88 changes: 22 additions & 66 deletions src/standard_normal_table.js
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Expand Up @@ -8,74 +8,30 @@
* above, or between values on the standard normal distribution, and by
* extension, any normal distribution.
*
* The probabilities are taken from http://en.wikipedia.org/wiki/Standard_normal_table
* The probabilities are calculated using formula from
* https://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function
* The table used is the cumulative, and not cumulative from 0 to mean
* (even though the latter has 5 digits precision, instead of 4).
*/
var standardNormalTable = [
/* z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 */
/* 0.0 */
0.5000, 0.5040, 0.5080, 0.5120, 0.5160, 0.5199, 0.5239, 0.5279, 0.5319, 0.5359,
/* 0.1 */
0.5398, 0.5438, 0.5478, 0.5517, 0.5557, 0.5596, 0.5636, 0.5675, 0.5714, 0.5753,
/* 0.2 */
0.5793, 0.5832, 0.5871, 0.5910, 0.5948, 0.5987, 0.6026, 0.6064, 0.6103, 0.6141,
/* 0.3 */
0.6179, 0.6217, 0.6255, 0.6293, 0.6331, 0.6368, 0.6406, 0.6443, 0.6480, 0.6517,
/* 0.4 */
0.6554, 0.6591, 0.6628, 0.6664, 0.6700, 0.6736, 0.6772, 0.6808, 0.6844, 0.6879,
/* 0.5 */
0.6915, 0.6950, 0.6985, 0.7019, 0.7054, 0.7088, 0.7123, 0.7157, 0.7190, 0.7224,
/* 0.6 */
0.7257, 0.7291, 0.7324, 0.7357, 0.7389, 0.7422, 0.7454, 0.7486, 0.7517, 0.7549,
/* 0.7 */
0.7580, 0.7611, 0.7642, 0.7673, 0.7704, 0.7734, 0.7764, 0.7794, 0.7823, 0.7852,
/* 0.8 */
0.7881, 0.7910, 0.7939, 0.7967, 0.7995, 0.8023, 0.8051, 0.8078, 0.8106, 0.8133,
/* 0.9 */
0.8159, 0.8186, 0.8212, 0.8238, 0.8264, 0.8289, 0.8315, 0.8340, 0.8365, 0.8389,
/* 1.0 */
0.8413, 0.8438, 0.8461, 0.8485, 0.8508, 0.8531, 0.8554, 0.8577, 0.8599, 0.8621,
/* 1.1 */
0.8643, 0.8665, 0.8686, 0.8708, 0.8729, 0.8749, 0.8770, 0.8790, 0.8810, 0.8830,
/* 1.2 */
0.8849, 0.8869, 0.8888, 0.8907, 0.8925, 0.8944, 0.8962, 0.8980, 0.8997, 0.9015,
/* 1.3 */
0.9032, 0.9049, 0.9066, 0.9082, 0.9099, 0.9115, 0.9131, 0.9147, 0.9162, 0.9177,
/* 1.4 */
0.9192, 0.9207, 0.9222, 0.9236, 0.9251, 0.9265, 0.9279, 0.9292, 0.9306, 0.9319,
/* 1.5 */
0.9332, 0.9345, 0.9357, 0.9370, 0.9382, 0.9394, 0.9406, 0.9418, 0.9429, 0.9441,
/* 1.6 */
0.9452, 0.9463, 0.9474, 0.9484, 0.9495, 0.9505, 0.9515, 0.9525, 0.9535, 0.9545,
/* 1.7 */
0.9554, 0.9564, 0.9573, 0.9582, 0.9591, 0.9599, 0.9608, 0.9616, 0.9625, 0.9633,
/* 1.8 */
0.9641, 0.9649, 0.9656, 0.9664, 0.9671, 0.9678, 0.9686, 0.9693, 0.9699, 0.9706,
/* 1.9 */
0.9713, 0.9719, 0.9726, 0.9732, 0.9738, 0.9744, 0.9750, 0.9756, 0.9761, 0.9767,
/* 2.0 */
0.9772, 0.9778, 0.9783, 0.9788, 0.9793, 0.9798, 0.9803, 0.9808, 0.9812, 0.9817,
/* 2.1 */
0.9821, 0.9826, 0.9830, 0.9834, 0.9838, 0.9842, 0.9846, 0.9850, 0.9854, 0.9857,
/* 2.2 */
0.9861, 0.9864, 0.9868, 0.9871, 0.9875, 0.9878, 0.9881, 0.9884, 0.9887, 0.9890,
/* 2.3 */
0.9893, 0.9896, 0.9898, 0.9901, 0.9904, 0.9906, 0.9909, 0.9911, 0.9913, 0.9916,
/* 2.4 */
0.9918, 0.9920, 0.9922, 0.9925, 0.9927, 0.9929, 0.9931, 0.9932, 0.9934, 0.9936,
/* 2.5 */
0.9938, 0.9940, 0.9941, 0.9943, 0.9945, 0.9946, 0.9948, 0.9949, 0.9951, 0.9952,
/* 2.6 */
0.9953, 0.9955, 0.9956, 0.9957, 0.9959, 0.9960, 0.9961, 0.9962, 0.9963, 0.9964,
/* 2.7 */
0.9965, 0.9966, 0.9967, 0.9968, 0.9969, 0.9970, 0.9971, 0.9972, 0.9973, 0.9974,
/* 2.8 */
0.9974, 0.9975, 0.9976, 0.9977, 0.9977, 0.9978, 0.9979, 0.9979, 0.9980, 0.9981,
/* 2.9 */
0.9981, 0.9982, 0.9982, 0.9983, 0.9984, 0.9984, 0.9985, 0.9985, 0.9986, 0.9986,
/* 3.0 */
0.9987, 0.9987, 0.9987, 0.9988, 0.9988, 0.9989, 0.9989, 0.9989, 0.9990, 0.9990
];

var SQRT_2PI = Math.sqrt(2 * Math.PI);

function cumulativeDistribution(z) {
var sum = z,
tmp = z;

// 15 iterations are enough for 4-digit precision
for (var i = 1; i < 15; i++) {
tmp *= z * z / (2 * i + 1);
sum += tmp;
}
return Math.round((0.5 + (sum / SQRT_2PI) * Math.exp(-z * z / 2)) * 1e4) / 1e4;
}

var standardNormalTable = [];

for (var z = 0; z <= 3.09; z += 0.01) {
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where does 3.09 come from?

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It's the max the original table has. :) We can change to 3 and update the tests.

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yeah, the question is then why does the original table stop then...

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Probably because it's so close to 1 for values after 3 that the error becomes acceptable. See the graph here https://en.wikipedia.org/wiki/File:Normal_Distribution_CDF.svg, red line.

standardNormalTable.push(cumulativeDistribution(z));
}

module.exports = standardNormalTable;