docs: update README with C API documentation

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Author: anandkaranubc

lib/node_modules/@stdlib/stats/base/dists/negative-binomial/mgf/README.md

@@ -176,6 +176,106 @@ for ( i = 0; i < 10; i++ ) {
 
 <!-- /.examples -->
 
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dists/negative-binomial/mgf.h"
+```
+
+#### stdlib_base_negative_binomial_mgf( t, r, p )
+
+Evaluates the moment-generating function (MGF) for a negative binomial distribution.ion function (CDF) for an arcsine distribution.
+
+```c
+double out = stdlib_base_negative_binomial_mgf( 0.05, 20.0, 0.8 );
+// returns ~267.839
+```
+
+The function accepts the following arguments:
+
+-   **t**: `[in] double` input value.
+-   **r**: `[in] double` number of successes until experiment is stopped.
+-   **p**: `[in] double` success probability.
+
+```c
+double stdlib_base_negative_binomial_mgf(const double t, const double r, const double p );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dists/negative-binomial/mgf.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+static double random_uniform( const double min, const double max ) {
+    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+    return min + ( v * ( max - min ) );
+}
+
+int main( void ) {
+    double t;
+    double r;
+    double p;
+    double y;
+    int i;
+
+    for ( i = 0; i < 25; i++ ) {
+        t = random_uniform( -1.0, 1.0 );
+        r = random_uniform( 1.0, 10.0 ); // r must be positive
+        p = random_uniform( 0.0, 1.0 );  // p must be between 0 and 1
+        y = stdlib_base_negative_binomial_mgf( t, r, p );
+        printf( "t: %lf, r: %lf, p: %lf, MGF(t;r,p): %lf\n", t, r, p, y );
+    }
+
+    return 0;
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <section class="references">