fix: updated the reviewed changes

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Author: NishchayRajput

lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/README.md

@@ -149,8 +149,6 @@ for ( i = 0; i < 10; i++ ) {
 
 <!-- /.examples -->
 
-<!-- /.examples -->
-
 <!-- C interface documentation. -->
 
 * * *
@@ -179,7 +177,7 @@ for ( i = 0; i < 10; i++ ) {
 
 #### stdlib_base_dists_cauchy_quantile( p, x0, gamma )
 
-Evaluates the [quantile function][quantile-function] of a [Cauchy][cauchy-distribution] distribution with location parameter x0 and scale parameter gamma.
+Evaluates the [quantile function][quantile-function] of a [Cauchy][cauchy-distribution] distribution with location parameter `x0` and scale parameter `gamma`.
 
 ```c
 double out = stdlib_base_dists_cauchy_quantile( 0.3, 2.0, 2.0 );
@@ -188,7 +186,7 @@ double out = stdlib_base_dists_cauchy_quantile( 0.3, 2.0, 2.0 );
 
 The function accepts the following arguments:
 
--   **p**: `[in] double` probability
+-   **p**: `[in] double` probability.
 -   **x0**: `[in] double` location parameter.
 -   **gamma**: `[in] double` scale parameter.
 
@@ -226,18 +224,18 @@ static double random_uniform( const double min, const double max ) {
 }
 
 int main( void ) {
-    double p;
     double gamma;
     double x0;
     double y;
+    double p;
     int i;
 
     for ( i = 0; i < 25; i++ ) {
         p = random_uniform( 0.0, 1.0 );
         x0 = random_uniform( 0.0, 10.0 ) - 5.0;
         gamma = random_uniform( 0.0, 20.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
         y = stdlib_base_dists_cauchy_quantile( p, x0, gamma );
-        printf( "x0: %lf, gamma: %lf, F(x0;gamma): %lf\n", x0, gamma, y );
+        printf( "p: %lf, x0: %lf, γ: %lf, Q(p;x0,γ): %lf\n", p, x0, gamma, y );
     }
 }
 ```

lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/examples/c/example.c

@@ -27,17 +27,17 @@ static double random_uniform( const double min, const double max ) {
 }
 
 int main( void ) {
-	double p;
 	double gamma;
 	double x0;
 	double y;
+	double p;
 	int i;
 
 	for ( i = 0; i < 25; i++ ) {
 		p = random_uniform( 0.0, 1.0 );
 		x0 = random_uniform( 0.0, 10.0 ) - 5.0;
 		gamma = random_uniform( 0.0, 20.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
 		y = stdlib_base_dists_cauchy_quantile( p, x0, gamma );
-		printf( "x0: %lf, gamma: %lf, F(x0;gamma): %lf\n", x0, gamma, y );
+		printf( "p: %lf, x0: %lf, gamma: %lf, Q(p;x0,gamma): %lf\n", p, x0, gamma, y );
 	}
 }

lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/include/stdlib/stats/base/dists/cauchy/quantile.h

@@ -27,7 +27,7 @@ extern "C" {
 #endif
 
 /**
-* Returns the differential quantile of a Cauchy distribution.
+* Returns a quantile function for a Cauchy distribution with probaility `p`, location parameter `x0` and scale parameter `gamma`.
 */
 double stdlib_base_dists_cauchy_quantile( const double p, const double x0, const double gamma );
 

lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/src/main.c

@@ -22,9 +22,9 @@
 #include "stdlib/constants/float64/pi.h"
 
 /**
-* Returns the differential entropy of a Cauchy distribution.
+* Evaluates the quantile function for a Cauchy distribution with probability `p`, location parameter `x0` and scale parameter `gamma`.
 *
-* @param p        input value
+* @param p        input probability
 * @param x0       location parameter
 * @param gamma    scale parameter
 * @return         evaluated entropy

lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/test/test.native.js

@@ -101,7 +101,7 @@ tape( 'if provided a nonpositive `gamma`, the function always returns `NaN`', op
 	t.end();
 });
 
-tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` ( large `gamma`)', opts, function test( t ) {
+tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma` (large `gamma`)', opts, function test( t ) {
 	var expected;
 	var gamma;
 	var delta;
@@ -138,6 +138,29 @@ tape( 'the function evaluates the quantile function at `p` given `x0` and `gamma
 	var y;
 	var i;
 
+	/*
+	* Higher tolerance than EPS because Julia gives slightly different results for
+	* |x| ~<= 3*pi/4:
+	*
+	* Example 1:
+	* x = -1.35646279095478;
+	* Julia (tan):  -4.593961172862999
+	* stdlib (tan): -4.593961172863
+	* Mathematica:  -4.59396117286300026311049650877442413097818001966176559315
+	*
+	* Example 2:
+	* x = 1.4710248292410089
+	* Julia (tan):  9.989623320530624
+	* stdlib (tan): 9.989623320530626
+	* Mathematica:  9.989623320530629158499137574831736702146195199133529403233
+	*
+	* Example 3:
+	* x = 1.528545878614728
+	* Julia (tan):  23.654302824341386
+	* stdlib (tan): 23.65430282434139
+	* Mathematica:  23.65430282434144042648214719732782590575979471046811610915...
+	*/
+
 	expected = positiveMedian.expected;
 	p = positiveMedian.p;
 	x0 = positiveMedian.x0;