fix: return ln(sqrt(2/pi)) instead of NaN for x = 0 and k = 1 in stats/base/dists/chi/logpdf

lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/lib/factory.js

@@ -81,7 +81,13 @@ function factory( k ) {
 		if ( x < 0.0 || x === PINF ) {
 			return NINF;
 		}
-		out = ( ( 1.0-kh ) * LN2 ) + ( km1 * ln( x ) ) - ( (x*x) / 2.0 );
+		out = ( 1.0-kh ) * LN2;
+
+		// For `k = 1`, the `x^(k-1)` factor is `1` (including at `x = 0`), whereas `(k-1) * ln(x)` would evaluate to `0 * -infinity = NaN` at `x = 0`:
+		if ( km1 !== 0.0 ) {
+			out += km1 * ln( x );
+		}
+		out -= ( x*x ) / 2.0;
 		out -= gammaln( kh );
 		return out;
 	}

lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/lib/main.js

@@ -80,7 +80,13 @@ function logpdf( x, k ) {
 		return NINF;
 	}
 	kh = k / 2.0;
-	out = ( ( 1.0-kh ) * LN2 ) + ( ( k-1.0 ) * ln( x ) ) - ( (x*x) / 2.0 );
+	out = ( 1.0-kh ) * LN2;
+
+	// For `k = 1`, the `x^(k-1)` factor is `1` (including at `x = 0`), whereas `(k-1) * ln(x)` would evaluate to `0 * -infinity = NaN` at `x = 0`:
+	if ( k !== 1.0 ) {
+		out += ( k-1.0 ) * ln( x );
+	}
+	out -= ( x*x ) / 2.0;
 	out -= gammaln( kh );
 	return out;
 }

lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/src/main.c

@@ -49,7 +49,13 @@ double stdlib_base_dists_chi_logpdf( const double x, const double k ) {
 		return STDLIB_CONSTANT_FLOAT64_NINF;
 	}
 	kh = k / 2.0;
-	out = ( ( 1.0 - kh ) * STDLIB_CONSTANT_FLOAT64_LN2 ) + ( ( k - 1.0 ) * stdlib_base_ln( x ) ) - ( ( x * x ) / 2.0 );
+	out = ( 1.0 - kh ) * STDLIB_CONSTANT_FLOAT64_LN2;
+
+	// For `k = 1`, the `x^(k-1)` factor is `1` (including at `x = 0`), whereas `(k-1) * ln(x)` would evaluate to `0 * -infinity = NaN` at `x = 0`:
+	if ( k != 1.0 ) {
+		out += ( k - 1.0 ) * stdlib_base_ln( x );
+	}
+	out -= ( x * x ) / 2.0;
 	out -= stdlib_base_gammaln( kh );
 	return out;
 }

lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/test/test.factory.js

@@ -143,6 +143,25 @@ tape( 'the returned function returns `-Infinity` for all `x < 0`', function test
 	t.end();
 });
 
+tape( 'if provided `x = 0`, the created function returns `ln(sqrt(2/π))` when `k = 1`, `+Infinity` when `k < 1`, and `-Infinity` when `k > 1`', function test( t ) {
+	var logpdf;
+	var y;
+
+	logpdf = factory( 1.0 );
+	y = logpdf( 0.0 );
+	t.strictEqual( isAlmostSameValue( y, -0.22579135264472744, 1 ), true, 'returns expected value' );
+
+	logpdf = factory( 0.5 );
+	y = logpdf( 0.0 );
+	t.strictEqual( y, PINF, 'returns expected value' );
+
+	logpdf = factory( 2.0 );
+	y = logpdf( 0.0 );
+	t.strictEqual( y, NINF, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'the created function evaluates the logpdf for `x` given degrees of freedom `k`', function test( t ) {
 	var expected;
 	var logpdf;

lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/test/test.logpdf.js

@@ -115,6 +115,21 @@ tape( 'the function returns `-Infinity` for all `x < 0`', function test( t ) {
 	t.end();
 });
 
+tape( 'if provided `x = 0`, the function returns `ln(sqrt(2/π))` when `k = 1`, `+Infinity` when `k < 1`, and `-Infinity` when `k > 1`', function test( t ) {
+	var y;
+
+	y = logpdf( 0.0, 1.0 );
+	t.strictEqual( isAlmostSameValue( y, -0.22579135264472744, 1 ), true, 'returns expected value' );
+
+	y = logpdf( 0.0, 0.5 );
+	t.strictEqual( y, PINF, 'returns expected value' );
+
+	y = logpdf( 0.0, 2.0 );
+	t.strictEqual( y, NINF, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'the function evaluates the logpdf for `x` given degrees of freedom `k`', function test( t ) {
 	var expected;
 	var x;

lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/test/test.native.js

@@ -94,6 +94,21 @@ tape( 'if provided `-infinity` for `x` and a valid `k`, the function returns `-i
 	t.end();
 });
 
+tape( 'if provided `x = 0`, the function returns `ln(sqrt(2/π))` when `k = 1`, `+Infinity` when `k < 1`, and `-Infinity` when `k > 1`', opts, function test( t ) {
+	var y;
+
+	y = logpdf( 0.0, 1.0 );
+	t.strictEqual( isAlmostSameValue( y, -0.22579135264472744, 1 ), true, 'returns expected value' );
+
+	y = logpdf( 0.0, 0.5 );
+	t.strictEqual( y, PINF, 'returns expected value' );
+
+	y = logpdf( 0.0, 2.0 );
+	t.strictEqual( y, NINF, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'the function evaluates the logpdf for given `x` and `k`', opts, function test( t ) {
 	var expected;
 	var x;