<?php
namespace MathPHP\Probability\Distribution\Discrete;

use MathPHP\Functions\Support;

/**
 * Bernoulli distribution
 *
 * https://en.wikipedia.org/wiki/Bernoulli_distribution
 */
class Bernoulli extends Discrete
{
    /**
     * Distribution parameter bounds limits
     * p ∈ (0,1)
     * @var array
     */
    const PARAMETER_LIMITS = [
        'p' => '(0,1)',
        'q' => '[0,1)',
    ];

    /**
     * Distribution support bounds limits
     * k ∈ [0,1]
     * p ∈ (0,1)
     * @var array
     */
    const SUPPORT_LIMITS = [
        'k' => '[0,1]',
    ];

    /** @var float probability of success */
    protected $p;

    /** @var float */
    protected $q;

    /**
     * Constructor
     *
     * @param float $p success probability  0 < p < 1
     */
    public function __construct(float $p)
    {
        $q = 1 - $p;
        parent::__construct($p, $q);
    }

    /**
     * Probability mass function
     *
     * q = (1 - p)  for k = 0
     * p            for k = 1
     *
     * @param  int $k number of successes  k ∈ {0, 1}
     *
     * @return float
     */
    public function pmf(int $k): float
    {
        Support::checkLimits(self::SUPPORT_LIMITS, ['k' => $k]);

        if ($k === 0) {
            return $this->q;
        } else {
            return $this->p;
        }
    }
    /**
     * Cumulative distribution function
     *
     * 0      for k < 0
     * 1 - p  for 0 ≤ k < 1
     * 1      for k ≥ 1
     *
     * @param  int $k number of successes  k ∈ {0, 1}
     *
     * @return float
     */
    public function cdf(int $k): float
    {
        if ($k < 0) {
            return 0;
        }
        if ($k < 1) {
            return 1 - $this->p;
        }
        return 1;
    }

    /**
     * Mean of the distribution
     *
     * μ = p
     *
     * @return float
     */
    public function mean(): float
    {
        return $this->p;
    }

    /**
     * Median of the distribution
     *
     * 0    for p < ½
     * ½    for p = ½
     * 1    for p > ½
     *
     * @return float
     */
    public function median(): float
    {
        $p = $this->p;
        $½ = 0.5;

        if ($p < $½) {
            return 0;
        }
        if ($p == $½) {
            return $½;
        }
        return 1;
    }

    /**
     * Mode of the distribution
     *
     * 0    for p < ½
     * 0,1  for p = ½
     * 1    for p > ½
     *
     * @return float[]
     */
    public function mode(): array
    {
        $p = $this->p;
        $½ = 0.5;

        if ($p < $½) {
            return [0];
        }
        if ($p == $½) {
            return [0, 1];
        }
        return [1];
    }

    /**
     * Variance of the distribution
     *
     * σ² = p(1 - p) = pq
     *
     * @return float
     */
    public function variance(): float
    {
        return $this->p * $this->q;
    }
}
