Minor improvements.

src/LinearAlgebra/VandermondeMatrix.php

@@ -25,8 +25,8 @@ class VandermondeMatrix extends Matrix
     /**
      * Create the Vandermonde Matrix from a simple array.
      *
-     * @param $M array (α₁, α₂, α₃ ⋯ αm)
-     * @param $n int
+     * @param array $M (α₁, α₂, α₃ ⋯ αm)
+     * @param int   $n
      */
     public function __construct(array $M, int $n)
     {

src/NumericalAnalysis/Interpolation/NevillesMethod.php

@@ -31,7 +31,7 @@ class NevillesMethod extends Interpolation
      *                                (point) contains precisely two numbers, an x and y.
      *                                Example array: [[1,2], [2,3], [3,4]].
      *                                Example callback: function($x) {return $x**2;}
-     * @param numbers  ... $args The arguments of our callback function: start,
+     * @param number   ... $args The arguments of our callback function: start,
      *                           end, and n. Example: approximate($source, 0, 8, 5).
      *                           If $source is a set of points, do not input any
      *                           $args. Example: approximate($source).

src/NumericalAnalysis/Interpolation/NewtonPolynomialForward.php

@@ -29,7 +29,7 @@ class NewtonPolynomialForward extends Interpolation
      *                           (point) contains precisely two numbers, an x and y.
      *                           Example array: [[1,2], [2,3], [3,4]].
      *                           Example callback: function($x) {return $x**2;}
-     * @param numbers  ... $args The arguments of our callback function: start,
+     * @param number   ... $args The arguments of our callback function: start,
      *                           end, and n. Example: approximate($source, 0, 8, 5).
      *                           If $source is a set of points, do not input any
      *                           $args. Example: approximate($source).

src/Probability/Distribution/Continuous/ChiSquared.php

@@ -28,13 +28,13 @@ class ChiSquared extends Continuous
         'x' => '[0,∞)',
     ];
 
-    /** @var number Degrees of Freedom Parameter */
+    /** @var float Degrees of Freedom Parameter */
     protected $k;
 
     /**
      * Constructor
      *
-     * @param number $k degrees of freedom parameter k >= 1
+     * @param float $k degrees of freedom parameter k >= 1
      */
     public function __construct($k)
     {
@@ -52,7 +52,7 @@ public function __construct($k)
      *
      * @param float $x point at which to evaluate > 0
      *
-     * @return number probability
+     * @return float probability
      */
     public function pdf(float $x)
     {
@@ -86,7 +86,7 @@ public function pdf(float $x)
      *
      * @param float $x Chi-square critical value (CV) > 0
      *
-     * @return number cumulative probability
+     * @return float cumulative probability
      */
     public function cdf(float $x)
     {
@@ -108,7 +108,7 @@ public function cdf(float $x)
      *
      * μ = k
      *
-     * @return int k
+     * @return float k
      */
     public function mean()
     {

src/Probability/Distribution/Continuous/Continuous.php

@@ -18,7 +18,7 @@ abstract class Continuous extends \MathPHP\Probability\Distribution\Distribution
      * @param float $target   The area for which we are trying to find the $x
      *
      * @todo check the parameter ranges.
-     * @return $number
+     * @return number
      */
     public function inverse(float $target)
     {

src/Probability/Distribution/Continuous/DiracDelta.php

@@ -48,7 +48,7 @@ public function __construct()
      *
      * @param float $x
      *
-     * @return number probability
+     * @return float probability
      */
     public function pdf(float $x): float
     {

src/Probability/Distribution/Discrete/Uniform.php

@@ -82,7 +82,7 @@ public function pmf()
      *
      * Percentile n = b - a + 1
      *
-     * @param number $k percentile
+     * @param int $k percentile
      *
      * @return number
      */

src/Probability/Distribution/Distribution.php

@@ -8,7 +8,7 @@ abstract class Distribution
     /**
      * Constructor
      *
-     * @param number[] $params
+     * @param number $params
      */
     public function __construct(...$params)
     {

src/Probability/Distribution/Multivariate/Dirichlet.php

@@ -36,7 +36,7 @@ class Dirichlet
     /**
      * Constructor
      *
-     * @param loat[] $αs
+     * @param float[] $αs
      */
     public function __construct(array $αs)
     {
@@ -56,7 +56,7 @@ public function __construct(array $αs)
      *
      * where B(α) is the multivariate Beta function
      *
-     * @param array float[] $xs
+     * @param float[] $xs
      *
      * @return float
      *

src/Probability/Distribution/Table/StandardNormal.php

@@ -148,7 +148,7 @@ public static function getZScoreProbability(float $Z): float
     /**
      * Get Z score for confidence interval
      *
-     * @param  int $cl confidence level
+     * @param  string $cl confidence level
      *
      * @return float Z score
      *

src/SetTheory/Set.php

@@ -248,7 +248,7 @@ public function removeMulti(array $x): Set
      *
      * @param mixed $x
      *
-     * @return string
+     * @return string|null
      */
     protected function getKey($x)
     {

src/Statistics/Average.php

@@ -22,7 +22,7 @@ class Average
      *
      * @param array $numbers
      *
-     * @return number
+     * @return number|null
      */
     public static function mean(array $numbers)
     {
@@ -43,7 +43,7 @@ public static function mean(array $numbers)
      * @param array $numbers
      * @param array $weights
      *
-     * @return number
+     * @return number|null
      *
      * @throws Exception\BadDataException if the number of numbers and weights are not equal
      */
@@ -76,7 +76,7 @@ function ($xᵢ, $wᵢ) {
      *
      * @param array $numbers
      *
-     * @return number
+     * @return number|null
      */
     public static function median(array $numbers)
     {
@@ -123,7 +123,7 @@ public static function median(array $numbers)
      * @param array $numbers
      * @param int $k zero indexed
      *
-     * @return number
+     * @return number|null
      */
     public static function kthSmallest(array $numbers, int $k)
     {
@@ -243,7 +243,8 @@ public static function mode(array $numbers): array
      * Geometric mean = ⁿ√a₀a₁a₂ ⋯
      *
      * @param  array  $numbers
-     * @return number
+     *
+     * @return number|null
      */
     public static function geometricMean(array $numbers)
     {
@@ -264,7 +265,8 @@ public static function geometricMean(array $numbers)
      * https://en.wikipedia.org/wiki/Harmonic_mean
      *
      * @param  array  $numbers
-     * @return number
+     *
+     * @return number|null
      *
      * @throws Exception\BadDataException if there are negative numbers
      */

src/Statistics/Correlation.php

@@ -596,7 +596,7 @@ public static function describe(array $X, array $Y, bool $population = false): a
     public static function confidenceEllipse(array $X, array $Y, float $z, int $num_points = 11): array
     {
         $standardNormal = new StandardNormal();
-        $p  = 2 * $standardNormal->CDF($z) - 1;
+        $p  = 2 * $standardNormal->cdf($z) - 1;
         $chiSquared = new ChiSquared(2);
         $χ² = $chiSquared->inverse($p);
 

src/Statistics/Descriptive.php

@@ -22,7 +22,8 @@ class Descriptive
      * R = max x - min x
      *
      * @param array $numbers
-     * @return number
+     *
+     * @return number|null
      */
     public static function range(array $numbers)
     {
@@ -42,7 +43,8 @@ public static function range(array $numbers)
      *           2
      *
      * @param array $numbers
-     * @return number
+     *
+     * @return number|null
      */
     public static function midrange(array $numbers)
     {
@@ -78,7 +80,8 @@ public static function midrange(array $numbers)
      *
      * @param array $numbers
      * @param int   $ν degrees of freedom
-     * @return number
+     *
+     * @return number|null
      *
      * @throws Exception\OutOfBoundsException if degrees of freedom is ≤ 0
      */
@@ -214,7 +217,7 @@ function ($xᵢ, $wᵢ) use ($μw) {
      *              false returns SD (uses sample variance);
      *              Default is false (SD (sample variance))
      *
-     * @return number
+     * @return number|null
      *
      * @throws Exception\OutOfBoundsException
      */
@@ -261,7 +264,8 @@ public static function sd(array $numbers, bool $SD＋ = false)
      * N is the number of numbers in the population set
      *
      * @param array $numbers
-     * @return number
+     *
+     * @return number|null
      */
     public static function meanAbsoluteDeviation(array $numbers)
     {
@@ -294,7 +298,8 @@ function ($xᵢ) use ($x) {
      * x̄ is the median
      *
      * @param array $numbers
-     * @return number
+     *
+     * @return number|null
      */
     public static function medianAbsoluteDeviation(array $numbers)
     {
@@ -629,12 +634,12 @@ public static function describe(array $numbers, bool $population = false): array
             'quartiles'          => self::quartiles($numbers),
             'midhinge'           => self::midhinge($numbers),
             'skewness'           => $population ? RandomVariable::populationSkewness($numbers) : RandomVariable::skewness($numbers),
-            'ses'                => $n > 2 ? RandomVariable::SES($n) : null,
+            'ses'                => $n > 2 ? RandomVariable::ses($n) : null,
             'kurtosis'           => RandomVariable::kurtosis($numbers),
-            'sek'                => $n > 3 ? RandomVariable::SEK($n) : null,
+            'sek'                => $n > 3 ? RandomVariable::sek($n) : null,
             'sem'                => RandomVariable::standardErrorOfTheMean($numbers),
-            'ci_95'              => RandomVariable::confidenceInterval($μ, $n, $σ, 95),
-            'ci_99'              => RandomVariable::confidenceInterval($μ, $n, $σ, 99),
+            'ci_95'              => RandomVariable::confidenceInterval($μ, $n, $σ, '95'),
+            'ci_99'              => RandomVariable::confidenceInterval($μ, $n, $σ, '99'),
         ];
     }
 

src/Statistics/Distance.php

@@ -120,7 +120,7 @@ function ($qᵢ) {
 
         // ∑ P(i) log(P(i)/Q(i))
         $Dkl⟮P‖Q⟯ = array_sum(array_map(
-            function ($P, $Q) use ($p, $q) {
+            function ($P, $Q) {
                 return $P * log($P / $Q);
             },
             $p,

src/Statistics/RandomVariable.php

@@ -46,7 +46,7 @@ class RandomVariable
      * @param array $X list of numbers (random variable X)
      * @param int   $n n-th central moment to calculate
      *
-     * @return number n-th central moment
+     * @return number|null n-th central moment
      */
     public static function centralMoment(array $X, int $n)
     {
@@ -83,7 +83,7 @@ function ($xᵢ) use ($μ, $n) {
      *
      * @param array $X list of numbers (random variable X)
      *
-     * @return number
+     * @return number|null
      */
     public static function populationSkewness(array $X)
     {
@@ -117,7 +117,7 @@ public static function populationSkewness(array $X)
      *
      * @param array $X list of numbers (random variable X)
      *
-     * @return number
+     * @return number|null
      */
     public static function sampleSkewness(array $X)
     {
@@ -151,7 +151,7 @@ public static function sampleSkewness(array $X)
      *
      * @param array $X list of numbers (random variable X)
      *
-     * @return number
+     * @return number|null
      *
      * @throws Exception\OutOfBoundsException
      */
@@ -219,7 +219,7 @@ public static function ses(int $n): float
      *
      * @param array $X list of numbers (random variable X)
      *
-     * @return number
+     * @return number|null
      */
     public static function kurtosis(array $X)
     {
@@ -317,7 +317,7 @@ public static function sek(int $n): float
      *
      * @param array $X list of numbers (random variable X)
      *
-     * @return float
+     * @return float|null
      *
      * @throws Exception\OutOfBoundsException
      */
@@ -395,7 +395,7 @@ public static function confidenceInterval($μ, int $n, $σ, string $cl): array
      *
      * @param array $numbers
      *
-     * @return number
+     * @return number|null
      */
     public static function sumOfSquares(array $numbers)
     {
@@ -415,7 +415,7 @@ public static function sumOfSquares(array $numbers)
      *
      * @param  array  $numbers
      *
-     * @return number
+     * @return number|null
      */
     public static function sumOfSquaresDeviations(array $numbers)
     {

src/Statistics/Regression/Methods/LeastSquares.php

@@ -199,7 +199,7 @@ public function leverages(): array
     public function sumOfSquaresRegression(): float
     {
         if ($this->fit_constant == 1) {
-            return RandomVariable::sumOfSquaresDeviations($this->Yhat());
+            return RandomVariable::sumOfSquaresDeviations($this->yhat());
         }
         return array_sum(Single::square($this->reg_Yhat));
     }

src/Statistics/Regression/PowerLaw.php

@@ -30,6 +30,12 @@ class PowerLaw extends ParametricRegression
 {
     use Models\PowerModel, Methods\LeastSquares;
 
+    /** @var float */
+    protected $a;
+
+    /** @var float */
+    protected $b;
+
     /**
      * Calculate the regression parameters by least squares on linearized data
      * ln(y) = ln(A) + B*ln(x)

src/Statistics/Regression/Regression.php

@@ -20,7 +20,7 @@ abstract class Regression
 
     /**
      * Y values of the original points
-     * @var [type]
+     * @var array
      */
     protected $ys;