<?php

namespace MathPHP\Probability\Distribution\Table;

use MathPHP\Exception;

/**
 * Standard normal tables for Z and related methods
 *
 * A standard normal table, also called the unit normal table or Z table,
 * is a mathematical table for the values of Φ, which are the values of the
 * cumulative distribution function of the normal distribution.
 *
 * It is used to find the probability that a statistic is observed below,
 * above, or between values on the standard normal distribution, and by extension,
 * any normal distribution.
 *
 * Since probability tables cannot be printed for every normal distribution,
 * as there are an infinite variety of normal distributions,
 * it is common practice to convert a normal to a standard normal
 * and then use the standard normal table to find probabilities.
 *
 * https://en.wikipedia.org/wiki/Standard_normal_table
 *
 * This table is provided only for completeness. It is common for statistics
 * textbooks to include this table, so this library does as well. It is better
 * to use the standard normal distribution CDF function when a Z score is required.
 */
class StandardNormal
{
    /**
     * Z scores table - cumulative from mean
     * Contains positive and negative Z scores.
     * Negative z-score - value is to the left of the mean.
     * Positive z-score - value is to the right of the mean.
     * @var array
     */
    const Z_SCORES = [
    '-3.4' => [ 9 => 0.0002, 8 => 0.0003, 7 => 0.0003, 6 => 0.0003, 5 => 0.0003, 4 => 0.0003, 3 => 0.0003, 2 => 0.0003, 1 => 0.0003, 0 => 0.0003 ],
    '-3.3' => [ 9 => 0.0003, 8 => 0.0004, 7 => 0.0004, 6 => 0.0004, 5 => 0.0004, 4 => 0.0004, 3 => 0.0004, 2 => 0.0005, 1 => 0.0005, 0 => 0.0005 ],
    '-3.2' => [ 9 => 0.0005, 8 => 0.0005, 7 => 0.0005, 6 => 0.0006, 5 => 0.0006, 4 => 0.0006, 3 => 0.0006, 2 => 0.0006, 1 => 0.0007, 0 => 0.0007 ],
    '-3.1' => [ 9 => 0.0007, 8 => 0.0007, 7 => 0.0008, 6 => 0.0008, 5 => 0.0008, 4 => 0.0008, 3 => 0.0009, 2 => 0.0009, 1 => 0.0009, 0 => 0.0010 ],
    '-3.0' => [ 9 => 0.0010, 8 => 0.0010, 7 => 0.0011, 6 => 0.0011, 5 => 0.0011, 4 => 0.0012, 3 => 0.0012, 2 => 0.0013, 1 => 0.0013, 0 => 0.0013 ],
    '-2.9' => [ 9 => 0.0014, 8 => 0.0014, 7 => 0.0015, 6 => 0.0015, 5 => 0.0016, 4 => 0.0016, 3 => 0.0017, 2 => 0.0018, 1 => 0.0018, 0 => 0.0019 ],
    '-2.8' => [ 9 => 0.0019, 8 => 0.0020, 7 => 0.0021, 6 => 0.0021, 5 => 0.0022, 4 => 0.0023, 3 => 0.0023, 2 => 0.0024, 1 => 0.0025, 0 => 0.0026 ],
    '-2.7' => [ 9 => 0.0026, 8 => 0.0027, 7 => 0.0028, 6 => 0.0029, 5 => 0.0030, 4 => 0.0031, 3 => 0.0032, 2 => 0.0033, 1 => 0.0034, 0 => 0.0035 ],
    '-2.6' => [ 9 => 0.0036, 8 => 0.0037, 7 => 0.0038, 6 => 0.0039, 5 => 0.0040, 4 => 0.0041, 3 => 0.0043, 2 => 0.0044, 1 => 0.0045, 0 => 0.0047 ],
    '-2.5' => [ 9 => 0.0048, 8 => 0.0049, 7 => 0.0051, 6 => 0.0052, 5 => 0.0054, 4 => 0.0055, 3 => 0.0057, 2 => 0.0059, 1 => 0.0060, 0 => 0.0062 ],
    '-2.4' => [ 9 => 0.0064, 8 => 0.0066, 7 => 0.0068, 6 => 0.0069, 5 => 0.0071, 4 => 0.0073, 3 => 0.0075, 2 => 0.0078, 1 => 0.0080, 0 => 0.0082 ],
    '-2.3' => [ 9 => 0.0084, 8 => 0.0087, 7 => 0.0089, 6 => 0.0091, 5 => 0.0094, 4 => 0.0096, 3 => 0.0099, 2 => 0.0102, 1 => 0.0104, 0 => 0.0107 ],
    '-2.2' => [ 9 => 0.0110, 8 => 0.0113, 7 => 0.0116, 6 => 0.0119, 5 => 0.0122, 4 => 0.0125, 3 => 0.0129, 2 => 0.0132, 1 => 0.0136, 0 => 0.0139 ],
    '-2.1' => [ 9 => 0.0143, 8 => 0.0146, 7 => 0.0150, 6 => 0.0154, 5 => 0.0158, 4 => 0.0162, 3 => 0.0166, 2 => 0.0170, 1 => 0.0174, 0 => 0.0179 ],
    '-2.0' => [ 9 => 0.0183, 8 => 0.0188, 7 => 0.0192, 6 => 0.0197, 5 => 0.0202, 4 => 0.0207, 3 => 0.0212, 2 => 0.0217, 1 => 0.0222, 0 => 0.0228 ],
    '-1.9' => [ 9 => 0.0233, 8 => 0.0239, 7 => 0.0244, 6 => 0.0250, 5 => 0.0256, 4 => 0.0262, 3 => 0.0268, 2 => 0.0274, 1 => 0.0281, 0 => 0.0287 ],
    '-1.8' => [ 9 => 0.0294, 8 => 0.0301, 7 => 0.0307, 6 => 0.0314, 5 => 0.0322, 4 => 0.0329, 3 => 0.0336, 2 => 0.0344, 1 => 0.0351, 0 => 0.0359 ],
    '-1.7' => [ 9 => 0.0367, 8 => 0.0375, 7 => 0.0384, 6 => 0.0392, 5 => 0.0401, 4 => 0.0409, 3 => 0.0418, 2 => 0.0427, 1 => 0.0436, 0 => 0.0446 ],
    '-1.6' => [ 9 => 0.0455, 8 => 0.0465, 7 => 0.0475, 6 => 0.0485, 5 => 0.0495, 4 => 0.0505, 3 => 0.0516, 2 => 0.0526, 1 => 0.0537, 0 => 0.0548 ],
    '-1.5' => [ 9 => 0.0559, 8 => 0.0571, 7 => 0.0582, 6 => 0.0594, 5 => 0.0606, 4 => 0.0618, 3 => 0.0630, 2 => 0.0643, 1 => 0.0655, 0 => 0.0668 ],
    '-1.4' => [ 9 => 0.0681, 8 => 0.0694, 7 => 0.0708, 6 => 0.0721, 5 => 0.0735, 4 => 0.0749, 3 => 0.0764, 2 => 0.0778, 1 => 0.0793, 0 => 0.0808 ],
    '-1.3' => [ 9 => 0.0823, 8 => 0.0838, 7 => 0.0853, 6 => 0.0869, 5 => 0.0885, 4 => 0.0901, 3 => 0.0918, 2 => 0.0934, 1 => 0.0951, 0 => 0.0968 ],
    '-1.2' => [ 9 => 0.0985, 8 => 0.1003, 7 => 0.1020, 6 => 0.1038, 5 => 0.1056, 4 => 0.1075, 3 => 0.1093, 2 => 0.1112, 1 => 0.1131, 0 => 0.1151 ],
    '-1.1' => [ 9 => 0.1170, 8 => 0.1190, 7 => 0.1210, 6 => 0.1230, 5 => 0.1251, 4 => 0.1271, 3 => 0.1292, 2 => 0.1314, 1 => 0.1335, 0 => 0.1357 ],
    '-1.0' => [ 9 => 0.1379, 8 => 0.1401, 7 => 0.1423, 6 => 0.1446, 5 => 0.1469, 4 => 0.1492, 3 => 0.1515, 2 => 0.1539, 1 => 0.1562, 0 => 0.1587 ],
    '-0.9' => [ 9 => 0.1611, 8 => 0.1635, 7 => 0.1660, 6 => 0.1685, 5 => 0.1711, 4 => 0.1736, 3 => 0.1762, 2 => 0.1788, 1 => 0.1814, 0 => 0.1841 ],
    '-0.8' => [ 9 => 0.1867, 8 => 0.1894, 7 => 0.1922, 6 => 0.1949, 5 => 0.1977, 4 => 0.2005, 3 => 0.2033, 2 => 0.2061, 1 => 0.2090, 0 => 0.2119 ],
    '-0.7' => [ 9 => 0.2148, 8 => 0.2177, 7 => 0.2206, 6 => 0.2236, 5 => 0.2266, 4 => 0.2296, 3 => 0.2327, 2 => 0.2358, 1 => 0.2389, 0 => 0.2420 ],
    '-0.6' => [ 9 => 0.2451, 8 => 0.2483, 7 => 0.2514, 6 => 0.2546, 5 => 0.2578, 4 => 0.2611, 3 => 0.2643, 2 => 0.2676, 1 => 0.2709, 0 => 0.2743 ],
    '-0.5' => [ 9 => 0.2776, 8 => 0.2810, 7 => 0.2843, 6 => 0.2877, 5 => 0.2912, 4 => 0.2946, 3 => 0.2981, 2 => 0.3015, 1 => 0.3050, 0 => 0.3085 ],
    '-0.4' => [ 9 => 0.3121, 8 => 0.3156, 7 => 0.3192, 6 => 0.3228, 5 => 0.3264, 4 => 0.3300, 3 => 0.3336, 2 => 0.3372, 1 => 0.3409, 0 => 0.3446 ],
    '-0.3' => [ 9 => 0.3483, 8 => 0.3520, 7 => 0.3557, 6 => 0.3594, 5 => 0.3632, 4 => 0.3669, 3 => 0.3707, 2 => 0.3745, 1 => 0.3783, 0 => 0.3821 ],
    '-0.2' => [ 9 => 0.3829, 8 => 0.3897, 7 => 0.3936, 6 => 0.3974, 5 => 0.4013, 4 => 0.4052, 3 => 0.4090, 2 => 0.4129, 1 => 0.4168, 0 => 0.4207 ],
    '-0.1' => [ 9 => 0.4247, 8 => 0.4286, 7 => 0.4325, 6 => 0.4364, 5 => 0.4404, 4 => 0.4443, 3 => 0.4483, 2 => 0.4522, 1 => 0.4562, 0 => 0.4602 ],
    '-0.0' => [ 9 => 0.4641, 8 => 0.4681, 7 => 0.4721, 6 => 0.4761, 5 => 0.4801, 4 => 0.4840, 3 => 0.4880, 2 => 0.4920, 1 => 0.4960, 0 => 0.5000 ],
     '0.0' => [ 0 => 0.50000, 1 => 0.50399, 2 => 0.50798, 3 => 0.51197, 4 => 0.51595, 5 => 0.51994, 6 => 0.52392, 7 => 0.52790, 8 => 0.53188, 9 => 0.53586 ],
     '0.1' => [ 0 => 0.53980, 1 => 0.54380, 2 => 0.54776, 3 => 0.55172, 4 => 0.55567, 5 => 0.55966, 6 => 0.56360, 7 => 0.56749, 8 => 0.57142, 9 => 0.57535 ],
     '0.2' => [ 0 => 0.57930, 1 => 0.58317, 2 => 0.58706, 3 => 0.59095, 4 => 0.59483, 5 => 0.59871, 6 => 0.60257, 7 => 0.60642, 8 => 0.61026, 9 => 0.61409 ],
     '0.3' => [ 0 => 0.61791, 1 => 0.62172, 2 => 0.62552, 3 => 0.62930, 4 => 0.63307, 5 => 0.63683, 6 => 0.64058, 7 => 0.64431, 8 => 0.64803, 9 => 0.65173 ],
     '0.4' => [ 0 => 0.65542, 1 => 0.65910, 2 => 0.66276, 3 => 0.66640, 4 => 0.67003, 5 => 0.67364, 6 => 0.67724, 7 => 0.68082, 8 => 0.68439, 9 => 0.68793 ],
     '0.5' => [ 0 => 0.69146, 1 => 0.69497, 2 => 0.69847, 3 => 0.70194, 4 => 0.70540, 5 => 0.70884, 6 => 0.71226, 7 => 0.71566, 8 => 0.71904, 9 => 0.72240 ],
     '0.6' => [ 0 => 0.72575, 1 => 0.72907, 2 => 0.73237, 3 => 0.73565, 4 => 0.73891, 5 => 0.74215, 6 => 0.74537, 7 => 0.74857, 8 => 0.75175, 9 => 0.75490 ],
     '0.7' => [ 0 => 0.75804, 1 => 0.76115, 2 => 0.76424, 3 => 0.76730, 4 => 0.77035, 5 => 0.77337, 6 => 0.77637, 7 => 0.77935, 8 => 0.78230, 9 => 0.78524 ],
     '0.8' => [ 0 => 0.78814, 1 => 0.79103, 2 => 0.79389, 3 => 0.79673, 4 => 0.79955, 5 => 0.80234, 6 => 0.80511, 7 => 0.80785, 8 => 0.81057, 9 => 0.81327 ],
     '0.9' => [ 0 => 0.81594, 1 => 0.81859, 2 => 0.82121, 3 => 0.82381, 4 => 0.82639, 5 => 0.82894, 6 => 0.83147, 7 => 0.83398, 8 => 0.83646, 9 => 0.83891 ],
     '1.0' => [ 0 => 0.84134, 1 => 0.84375, 2 => 0.84614, 3 => 0.84849, 4 => 0.85083, 5 => 0.85314, 6 => 0.85543, 7 => 0.85769, 8 => 0.85993, 9 => 0.86214 ],
     '1.1' => [ 0 => 0.86433, 1 => 0.86650, 2 => 0.86864, 3 => 0.87076, 4 => 0.87286, 5 => 0.87493, 6 => 0.87698, 7 => 0.87900, 8 => 0.88100, 9 => 0.88298 ],
     '1.2' => [ 0 => 0.88493, 1 => 0.88686, 2 => 0.88877, 3 => 0.89065, 4 => 0.89251, 5 => 0.89435, 6 => 0.89617, 7 => 0.89796, 8 => 0.89973, 9 => 0.90147 ],
     '1.3' => [ 0 => 0.90320, 1 => 0.90490, 2 => 0.90658, 3 => 0.90824, 4 => 0.90988, 5 => 0.91149, 6 => 0.91308, 7 => 0.91466, 8 => 0.91621, 9 => 0.91774 ],
     '1.4' => [ 0 => 0.91924, 1 => 0.92073, 2 => 0.92220, 3 => 0.92364, 4 => 0.92507, 5 => 0.92647, 6 => 0.92785, 7 => 0.92922, 8 => 0.93056, 9 => 0.93189 ],
     '1.5' => [ 0 => 0.93319, 1 => 0.93448, 2 => 0.93574, 3 => 0.93699, 4 => 0.93822, 5 => 0.93943, 6 => 0.94062, 7 => 0.94179, 8 => 0.94295, 9 => 0.94408 ],
     '1.6' => [ 0 => 0.94520, 1 => 0.94630, 2 => 0.94738, 3 => 0.94845, 4 => 0.94950, 5 => 0.95053, 6 => 0.95154, 7 => 0.95254, 8 => 0.95352, 9 => 0.95449 ],
     '1.7' => [ 0 => 0.95543, 1 => 0.95637, 2 => 0.95728, 3 => 0.95818, 4 => 0.95907, 5 => 0.95994, 6 => 0.96080, 7 => 0.96164, 8 => 0.96246, 9 => 0.96327 ],
     '1.8' => [ 0 => 0.96407, 1 => 0.96485, 2 => 0.96562, 3 => 0.96638, 4 => 0.96712, 5 => 0.96784, 6 => 0.96856, 7 => 0.96926, 8 => 0.96995, 9 => 0.97062 ],
     '1.9' => [ 0 => 0.97128, 1 => 0.97193, 2 => 0.97257, 3 => 0.97320, 4 => 0.97381, 5 => 0.97441, 6 => 0.97500, 7 => 0.97558, 8 => 0.97615, 9 => 0.97670 ],
     '2.0' => [ 0 => 0.97725, 1 => 0.97778, 2 => 0.97831, 3 => 0.97882, 4 => 0.97932, 5 => 0.97982, 6 => 0.98030, 7 => 0.98077, 8 => 0.98124, 9 => 0.98169 ],
     '2.1' => [ 0 => 0.98214, 1 => 0.98257, 2 => 0.98300, 3 => 0.98341, 4 => 0.98382, 5 => 0.98422, 6 => 0.98461, 7 => 0.98500, 8 => 0.98537, 9 => 0.98574 ],
     '2.2' => [ 0 => 0.98610, 1 => 0.98645, 2 => 0.98679, 3 => 0.98713, 4 => 0.98745, 5 => 0.98778, 6 => 0.98809, 7 => 0.98840, 8 => 0.98870, 9 => 0.98899 ],
     '2.3' => [ 0 => 0.98928, 1 => 0.98956, 2 => 0.98983, 3 => 0.99010, 4 => 0.99036, 5 => 0.99061, 6 => 0.99086, 7 => 0.99111, 8 => 0.99134, 9 => 0.99158 ],
     '2.4' => [ 0 => 0.99180, 1 => 0.99202, 2 => 0.99224, 3 => 0.99245, 4 => 0.99266, 5 => 0.99286, 6 => 0.99305, 7 => 0.99324, 8 => 0.99343, 9 => 0.99361 ],
     '2.5' => [ 0 => 0.99379, 1 => 0.99396, 2 => 0.99413, 3 => 0.99430, 4 => 0.99446, 5 => 0.99461, 6 => 0.99477, 7 => 0.99492, 8 => 0.99506, 9 => 0.99520 ],
     '2.6' => [ 0 => 0.99534, 1 => 0.99547, 2 => 0.99560, 3 => 0.99573, 4 => 0.99585, 5 => 0.99598, 6 => 0.99609, 7 => 0.99621, 8 => 0.99632, 9 => 0.99643 ],
     '2.7' => [ 0 => 0.99653, 1 => 0.99664, 2 => 0.99674, 3 => 0.99683, 4 => 0.99693, 5 => 0.99702, 6 => 0.99711, 7 => 0.99720, 8 => 0.99728, 9 => 0.99736 ],
     '2.8' => [ 0 => 0.99744, 1 => 0.99752, 2 => 0.99760, 3 => 0.99767, 4 => 0.99774, 5 => 0.99781, 6 => 0.99788, 7 => 0.99795, 8 => 0.99801, 9 => 0.99807 ],
     '2.9' => [ 0 => 0.99813, 1 => 0.99819, 2 => 0.99825, 3 => 0.99831, 4 => 0.99836, 5 => 0.99841, 6 => 0.99846, 7 => 0.99851, 8 => 0.99856, 9 => 0.99861 ],
     '3.0' => [ 0 => 0.99865, 1 => 0.99869, 2 => 0.99874, 3 => 0.99878, 4 => 0.99882, 5 => 0.99886, 6 => 0.99889, 7 => 0.99893, 8 => 0.99896, 9 => 0.99900 ],
    ];

    /**
     * Get Z score probability (Φ)
     *
     * @param float $Z
     *
     * @return float probability
     *
     * @throws Exception\BadDataException
     */
    public static function getZScoreProbability(float $Z): float
    {
        if (!preg_match('/^ (\-? \d [.] \d) (\d) $/x', sprintf('%1.2f', $Z), $matches)) {
            throw new Exception\BadParameterException("Z does not match format X.XX: $Z");
        }
        list( $z, $＋0．0x ) = [ $matches[1], $matches[2] ];
        return self::Z_SCORES[$z][$＋0．0x];
    }

    /**
     * Z scores for confidence intervals
     * Key: confidence level %
     * Value: Z score
     * @var array
     */
    const Z_SCORES_FOR_CONFIDENCE_INTERVALS = [
        50     => 0.67449,
        70     => 1.04,
        75     => 1.15035,
        80     => 1.282,
        85     => 1.44,
        90     => 1.64485,
        92     => 1.75,
        95     => 1.95996,
        96     => 2.05,
        97     => 2.17009,
        98     => 2.326,
        99     => 2.57583,
        '99.5' => 2.81,
        '99.8' => 3.08,
        '99.9' => 3.29053,
    ];

    /**
     * Get Z score for confidence interval
     *
     * @param  string $cl confidence level
     *
     * @return float Z score
     *
     * @throws Exception\BadDataException
     */
    public static function getZScoreForConfidenceInterval(string $cl): float
    {
        if (!array_key_exists($cl, self::Z_SCORES_FOR_CONFIDENCE_INTERVALS)) {
            throw new Exception\BadDataException('Not a valid confidence level');
        }
        return self::Z_SCORES_FOR_CONFIDENCE_INTERVALS[$cl];
    }
}