feat: add implementation of stats/base/dists/erlang/logcdf

lib/node_modules/@stdlib/stats/base/dists/erlang/logcdf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# Logarithm of Cumulative Distribution Function
+
+> Evaluate the natural logarithm of the cumulative distribution function (CDF) for an [Erlang][erlang-distribution] distribution.
+
+<section class="intro">
+
+The [cumulative distribution function][cdf] for a [Erlang][erlang-distribution] random variable is
+
+<!-- <equation class="equation" label="eq:erlang_cdf" align="center" raw="F(x; k,\lambda) = 1 - \sum_{n=0}^{k-1}\frac{1}{n!}e^{-\lambda x}(\lambda x)^n" alt="Cumulative distribution function for a Erlang distribution."> -->
+
+```math
+F(x; k,\lambda) = 1 - \sum_{n=0}^{k-1}\frac{1}{n!}e^{-\lambda x}(\lambda x)^n
+```
+
+<!-- <div class="equation" align="center" data-raw-text="F(x; k,\lambda) = 1 - \sum_{n=0}^{k-1}\frac{1}{n!}e^{-\lambda x}(\lambda x)^n" data-equation="eq:erlang_cdf">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/erlang/cdf/docs/img/equation_erlang_cdf.svg" alt="Cumulative distribution function for a Erlang distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `k` is the nonnegative integer shape parameter and `lambda > 0` is the rate parameter. The [Erlang][erlang-distribution] distribution is a special case of the gamma distribution, as `k` is constrained to the natural numbers.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var logcdf = require( '@stdlib/stats/base/dists/erlang/logcdf' );
+```
+
+#### logcdf( x, k, lambda )
+
+Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for an [Erlang][erlang-distribution] distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).
+
+```javascript
+var y = logcdf( 2.0, 1, 1.0 );
+// returns ~-0.145
+
+y = logcdf( 2.0, 3, 1.0 );
+// returns ~-1.129
+
+y = logcdf( -1.0, 2, 2.0 );
+// returns -Infinity
+
+y = logcdf( -Infinity, 4, 2.0 );
+// returns -Infinity
+
+y = logcdf( +Infinity, 4, 2.0 );
+// returns 0.0
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = logcdf( NaN, 1, 1.0 );
+// returns NaN
+
+y = logcdf( 0.0, NaN, 1.0 );
+// returns NaN
+
+y = logcdf( 0.0, 1, NaN );
+// returns NaN
+```
+
+If not provided a nonnegative integer for `k`, the function returns `NaN`.
+
+```javascript
+var y = logcdf( 2.0, -2, 0.5 );
+// returns NaN
+
+y = logcdf( 2.0, 0.5, 0.5 );
+// returns NaN
+```
+
+If provided `k = 0`, the function evaluates the logarithm of the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.
+
+```javascript
+var y = logcdf( 2.0, 0.0, 2.0 );
+// returns -0.0
+
+y = logcdf( -2.0, 0.0, 2.0 );
+// returns -Infinity
+
+y = logcdf( 0.0, 0.0, 2.0 );
+// returns -0.0
+```
+
+If provided `lambda <= 0`, the function returns `NaN`.
+
+```javascript
+var y = logcdf( 2.0, 1, 0.0 );
+// returns NaN
+
+y = logcdf( 2.0, 1, -5.0 );
+// returns NaN
+```
+
+#### logcdf.factory( k, lambda )
+
+Returns a `function` for evaluating the [cumulative distribution function][cdf] for an [Erlang][erlang-distribution] distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).
+
+```javascript
+var mylogcdf = logcdf.factory( 2, 0.5 );
+
+var y = mylogcdf( 6.0 );
+// returns ~-0.222
+
+y = mylogcdf( 2.0 );
+// returns ~-1.331
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var logcdf = require( '@stdlib/stats/base/dists/erlang/logcdf' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var x = uniform( 20, 0.0, 10.0, opts );
+var k = discreteUniform( 20, 0, 10, opts );
+var lambda = uniform( 20, 0.0, 5.0, opts );
+
+logEachMap( 'x: %lf, k: %d, λ: %lf, F(x;k,λ): %lf', x, k, lambda, logcdf );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
+
+[erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_distribution
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/erlang/logcdf/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var logcdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var lambda;
+	var len;
+	var k;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	x = uniform( len, 0.0, 100.0 );
+	k = discreteUniform( len, 0.0, 100.0 );
+	lambda = uniform( len, EPS, 20.0 );
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = logcdf( x[ i % len ], k[ i % len ], lambda[ i % len ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( format( '%s::factory', pkg ), function benchmark( b ) {
+	var mylogpdf;
+	var lambda;
+	var len;
+	var k;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	k = 2.0;
+	lambda = 1.5;
+	x = uniform( len, EPS, 50.0 );
+	mylogpdf = logcdf.factory( k, lambda );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mylogpdf( x[ i % len ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/stats/base/dists/erlang/logcdf/docs/repl.txt

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+
+{{alias}}( x, k, λ )
+    Evaluates the natural logarithm of cumulative distribution function
+    (CDF) for an Erlang distribution with shape parameter `k` and rate
+    parameter `λ` at a value `x`.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If not provided a nonnegative integer for `k`, the function returns `NaN`.
+
+    If provided a non-positive value for `λ`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    k: number
+        Shape parameter.
+
+    λ: number
+        Rate parameter.
+
+    Returns
+    -------
+    out: number
+        Evaluated logCDF.
+
+    Examples
+    --------
+    > var y = {{alias}}( 2.0, 1, 1.0 )
+    ~-0.145
+    > y = {{alias}}( 2.0, 3, 1.0 )
+    ~-1.129
+    > y = {{alias}}( 2.0, 2.5, 1.0 )
+    NaN
+    > y = {{alias}}( -1.0, 2, 2.0 )
+    -Infinity
+    > y = {{alias}}( {{alias:@stdlib/constants/float64/pinf}}, 4, 2.0 )
+    0.0
+    > y = {{alias}}( {{alias:@stdlib/constants/float64/ninf}}, 4, 2.0 )
+    -Infinity
+    > y = {{alias}}( NaN, 0, 1.0 )
+    NaN
+    > y = {{alias}}( 0.0, NaN, 1.0 )
+    NaN
+    > y = {{alias}}( 0.0, 0, NaN )
+    NaN
+    > y = {{alias}}( 2.0, -1, 1.0 )
+    NaN
+    > y = {{alias}}( 2.0, 1, -1.0 )
+    NaN
+
+
+{{alias}}.factory( k, λ )
+    Returns a function for evaluating the natural logarithm of cumulative
+    distribution function (CDF) of an Erlang distribution with shape parameter
+    `k` and rate parameter `λ`.
+
+    Parameters
+    ----------
+    k: number
+        Shape parameter.
+
+    λ: number
+        Rate parameter.
+
+    Returns
+    -------
+    logcdf: Function
+        Natural logarithm of cumulative distribution function (CDF).
+
+    Examples
+    --------
+    > var mycdf = {{alias}}.factory( 2, 0.5 );
+    > var y = mycdf( 6.0 )
+    ~-0.222
+    > y = mycdf( 2.0 )
+    ~-1.331
+
+    See Also
+    --------
+