fix: correct off-by-one in large-x series of math/base/special/gammainc

lib/node_modules/@stdlib/math/base/special/gammainc/lib/tgamma_i_large_x_series.js

@@ -44,7 +44,7 @@
 */
 function tgammaILargeXSeries( a1, x1 ) {
 	var result = 1.0;
-	var a = a1;
+	var a = a1 - 1.0;
 	var x = x1;
 	return next;
 

lib/node_modules/@stdlib/math/base/special/gammainc/src/main.c

@@ -700,7 +700,7 @@ static double sumSeries3( const double a, const double x ) {
 	double sum;
 	double ac;
 
-	ac = a;
+	ac = a - 1.0;
 	sum = 0.0;
 	result = 1.0;
 	counter = MAX_ITERATIONS;

lib/node_modules/@stdlib/math/base/special/gammainc/test/test.js

@@ -464,3 +464,15 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma
 	}
 	t.end();
 });
+
+tape( 'the function correctly evaluates the regularized incomplete gamma functions for large `x` when `s` is close to `x`', function test( t ) {
+	var actual;
+
+	// NOTE: expected values were computed using arbitrary-precision arithmetic with 60 digits of precision.
+	actual = gammainc( 1367.3436948118986, 1409.203708740708 );
+	t.strictEqual( ulpdiff( actual, 0.13190499189857088 ) <= 100, true, 'returns expected value within 100 ulp' );
+
+	actual = gammainc( 1001.0, 1000.5, true, true );
+	t.strictEqual( ulpdiff( actual, 0.48949191460024505 ) <= 10, true, 'returns expected value within 10 ulp' );
+	t.end();
+});

lib/node_modules/@stdlib/math/base/special/gammainc/test/test.native.js

@@ -473,3 +473,15 @@ tape( 'the function correctly evaluates the unregularized upper incomplete gamma
 	}
 	t.end();
 });
+
+tape( 'the function correctly evaluates the regularized incomplete gamma functions for large `x` when `s` is close to `x`', opts, function test( t ) {
+	var actual;
+
+	// NOTE: expected values were computed using arbitrary-precision arithmetic with 60 digits of precision.
+	actual = gammainc( 1367.3436948118986, 1409.203708740708, true, false );
+	t.strictEqual( ulpdiff( actual, 0.13190499189857088 ) <= 100, true, 'returns expected value within 100 ulp' );
+
+	actual = gammainc( 1001.0, 1000.5, true, true );
+	t.strictEqual( ulpdiff( actual, 0.48949191460024505 ) <= 10, true, 'returns expected value within 10 ulp' );
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/chisquare/cdf/test/test.cdf.js

@@ -116,3 +116,12 @@ tape( 'the function evaluates the cdf for `x` given degrees of freedom `k`', fun
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the cdf for large `k` when `x` is close to `k`', function test( t ) {
+	var y;
+
+	// NOTE: expected value was computed using arbitrary-precision arithmetic with 60 digits of precision.
+	y = cdf( 2500.0, 2400.0 );
+	t.strictEqual( isAlmostSameValue( y, 0.9241270884571916, 10 ), true, 'returns expected value' );
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/chisquare/cdf/test/test.native.js

@@ -105,3 +105,12 @@ tape( 'the function evaluates the cdf for `x` given `k`', opts, function test( t
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the cdf for large `k` when `x` is close to `k`', opts, function test( t ) {
+	var y;
+
+	// NOTE: expected value was computed using arbitrary-precision arithmetic with 60 digits of precision.
+	y = cdf( 2500.0, 2400.0 );
+	t.strictEqual( isAlmostSameValue( y, 0.9241270884571916, 10 ), true, 'returns expected value' );
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/poisson/cdf/test/test.cdf.js

@@ -153,3 +153,12 @@ tape( 'the function evaluates the cdf for `x` given large parameter `lambda`', f
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the cdf for large `lambda` when `x` is close to `lambda`', function test( t ) {
+	var y;
+
+	// NOTE: expected value was computed using arbitrary-precision arithmetic with 60 digits of precision.
+	y = cdf( 999.0, 1001.0 );
+	t.strictEqual( isAlmostSameValue( y, 0.4831885470702138, 30 ), true, 'returns expected value' );
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/poisson/cdf/test/test.native.js

@@ -166,3 +166,12 @@ tape( 'the function evaluates the cdf for `x` given large parameter `lambda`', o
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the cdf for large `lambda` when `x` is close to `lambda`', opts, function test( t ) {
+	var y;
+
+	// NOTE: expected value was computed using arbitrary-precision arithmetic with 60 digits of precision.
+	y = cdf( 999.0, 1001.0 );
+	t.strictEqual( isAlmostSameValue( y, 0.4831885470702138, 30 ), true, 'returns expected value' );
+	t.end();
+});