feat:C implementation of stats/base/dists/weibull/skewness

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---

Author: yuvi-mittal

lib/node_modules/@stdlib/stats/base/dists/weibull/skewness/src/main.c

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -19,32 +19,40 @@
 #include "stdlib/stats/base/dists/weibull/skewness.h"
 #include "stdlib/math/base/assert/is_nan.h"
 #include "stdlib/math/base/special/gamma.h"
-#include <math.h>
+#include "stdlib/math/base/special/pow.h"
+#include "stdlib/math/base/special/sqrt.h"
 
 /**
-* Evaluates the skewness for a Weibull distribution with shape parameter `k`.
+* Evaluates the skewness for a Weibull distribution with shape parameter `k` and scale parameter `lambda`.
 *
-* @param k    shape parameter (k > 0)
-* @return     skewness
+* @param k       shape parameter
+* @param lambda  scale parameter
+* @return        skewness of the distribution
 *
 * @example
-* double y = stdlib_base_dists_weibull_skewness( 1.5 );
-* // returns ~1.14
+* double y = stdlib_base_dists_weibull_skewness( 4.0, 12.0 );
+* // returns ~-0.087
 */
-double stdlib_base_dists_weibull_skewness( const double k ) {
-    if ( stdlib_base_is_nan( k ) || k <= 0.0 ) {
-        return 0.0/0.0; // NaN
-    }
+double stdlib_base_dists_weibull_skewness( const double k, const double lambda ) {
+	if (
+		stdlib_base_is_nan( k ) ||
+		stdlib_base_is_nan( lambda ) ||
+		k <= 0.0 ||
+		lambda <= 0.0
+	) {
+		return 0.0/0.0; // NaN
+	}
 
-    // Compute gamma-related terms:
-    double gamma1 = stdlib_base_gamma( 1.0 + ( 1.0 / k ) );
-    double gamma2 = stdlib_base_gamma( 1.0 + ( 2.0 / k ) );
-    double gamma3 = stdlib_base_gamma( 1.0 + ( 3.0 / k ) );
+	double gamma1 = stdlib_base_gamma( 1.0 + (3.0 / k) );
+	double gamma2 = stdlib_base_gamma( 1.0 + (2.0 / k) );
+	double gamma3 = stdlib_base_gamma( 1.0 + (1.0 / k) );
 
-    // Compute variance and mean terms:
-    double variance = gamma2 - ( gamma1 * gamma1 );
-    double stddev = sqrt( variance );
+	double mu = gamma3 * lambda;
+	double sigma2 = (gamma2 * lambda * lambda) - (mu * mu);
+	double sigma = stdlib_base_sqrt( sigma2 );
 
-    // Compute skewness:
-    return ( gamma3 - ( 3.0 * gamma1 * gamma2 ) + ( 2.0 * pow( gamma1, 3 ) ) ) / pow( stddev, 3 );
+	double numerator = (gamma1 * lambda * lambda * lambda) - (3.0 * mu * sigma2) - (mu * mu * mu);
+	double denominator = stdlib_base_pow( sigma, 3.0 );
+
+	return numerator / denominator;
 }