feat: add stats/base/dists/burr-type3/cdf

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lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var cdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var alpha;
+	var beta;
+	var len;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	x = uniform( len, 0.0, 10.0 );
+	alpha = uniform( len, 0.1, 100.0 );
+	beta = uniform( len, 0.1, 100.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cdf( x[ i % len ], alpha[ i % len ], beta[ 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( pkg+':factory', function benchmark( b ) {
+	var mycdf;
+	var len;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	x = uniform( len, 0.0, 10.0 );
+	mycdf = cdf.factory( 5.0, 6.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mycdf( 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/burr-type3/cdf/benchmark/python/benchmark.scipy.py

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+#!/usr/bin/env python
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2018 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.
+
+"""Benchmark scipy.stats.burr.cdf."""
+
+from __future__ import print_function
+import timeit
+
+NAME = "burr:cdf"
+REPEATS = 3
+ITERATIONS = 1000
+
+
+def print_version():
+    """Print the TAP version."""
+    print("TAP version 13")
+
+
+def print_summary(total, passing):
+    """Print the benchmark summary.
+
+    # Arguments
+
+    * `total`: total number of tests
+    * `passing`: number of passing tests
+
+    """
+    print("#")
+    print("1.." + str(total))  # TAP plan
+    print("# total " + str(total))
+    print("# pass  " + str(passing))
+    print("#")
+    print("# ok")
+
+
+def print_results(elapsed):
+    """Print benchmark results.
+
+    # Arguments
+
+    * `elapsed`: elapsed time (in seconds)
+
+    # Examples
+
+    ``` python
+    python> print_results(0.131009101868)
+    ```
+    """
+    rate = ITERATIONS / elapsed
+
+    print("  ---")
+    print("  iterations: " + str(ITERATIONS))
+    print("  elapsed: " + str(elapsed))
+    print("  rate: " + str(rate))
+    print("  ...")
+
+
+def benchmark():
+    """Run the benchmark and print benchmark results."""
+    setup = "from scipy.stats import burr; from random import random;"
+    stmt = "y = burr.cdf(random(), 100.56789, 55.54321)"
+
+    t = timeit.Timer(stmt, setup=setup)
+
+    print_version()
+
+    for i in range(REPEATS):
+        print("# python::" + NAME)
+        elapsed = t.timeit(number=ITERATIONS)
+        print_results(elapsed)
+        print("ok " + str(i+1) + " benchmark finished")
+
+    print_summary(REPEATS, REPEATS)
+
+
+def main():
+    """Run the benchmark."""
+    benchmark()
+
+
+if __name__ == "__main__":
+    main()

lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/docs/repl.txt

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+
+{{alias}}( x, α, β )
+    Evaluates the cumulative distribution function (CDF) for a
+    Burr (type III) distribution with first shape parameter
+    `α` and second shape parameter `β` at a value `x`.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If `α <= 0` or `β <= 0` or `x <= 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    α: number
+        First shape parameter.
+
+    β: number
+        Second shape parameter.
+
+    Returns
+    -------
+    out: number
+        Evaluated CDF.
+
+    Examples
+    --------
+    > var y = {{alias}}( 0.1, 1.0, 1.0 )
+    ~0.09
+    > y = {{alias}}( 0.2, 2.0, 2.0 )
+    ~0.0015
+    > y = {{alias}}( 0.8, 0.5, 0.5 )
+    ~0.69
+    > y = {{alias}}( 0.3, 0.5, 0.5 )
+    ~0.59
+
+    > y = {{alias}}( -0.5, 4.0, 2.0 )
+    NaN
+    > y = {{alias}}( 2.0, -1.0, 0.5 )
+    NaN
+    > y = {{alias}}( 2.0, 0.5, -1.0 )
+    NaN
+
+    > y = {{alias}}( NaN, 1.0, 1.0 )
+    NaN
+    > y = {{alias}}( 0.0, NaN, 1.0 )
+    NaN
+    > y = {{alias}}( 0.0, 1.0, NaN )
+    NaN
+
+
+{{alias}}.factory( α, β )
+    Returns a function for evaluating the cumulative distribution
+    function (CDF) of a Burr (type III) distribution with
+    first shape parameter `α` and second shape parameter `β`.
+
+    Parameters
+    ----------
+    α: number
+        First shape parameter.
+
+    β: number
+        Second shape parameter.
+
+    Returns
+    -------
+    cdf: Function
+        Cumulative distribution function (CDF).
+
+    Examples
+    --------
+    > var mycdf = {{alias}}.factory( 0.5, 0.5 );
+    > var y = mycdf( 0.8 )
+    ~0.69
+    > y = mycdf( 0.3 )
+    ~0.59
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Evaluates the cumulative distribution function (CDF) for a Burr (type III) distribution.
+*
+* @param x - input value
+* @returns evaluated CDF
+*/
+type Unary = ( x: number ) => number;
+
+/**
+* Interface for the cumulative distribution function (CDF) of a Burr (type III) distribution.
+*/
+interface CDF {
+	/**
+	* Evaluates the cumulative distribution function (CDF) for a Burr (type III) distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `x`.
+	*
+	* ## Notes
+	*
+	* -   If `alpha <= 0` or `beta <= 0` or `x <= 0`, the function returns `NaN`.
+	*
+	* @param x - input value
+	* @param alpha - first shape parameter
+	* @param beta - second shape parameter
+	* @returns evaluated CDF
+	*
+	* @example
+	* var y = cdf( 0.1, 1.0, 1.0 );
+	* // returns ~0.09
+	*
+	* @example
+	* var y = cdf( 0.2, 2.0, 2.0 );
+	* // returns ~0.0015
+	*
+	* @example
+	* var y = cdf( 0.4, 4.0, 4.0 );
+	* // returns ~3.88e-7
+	*
+	* @example
+	* var y = cdf( 1.0, 0.1, 1.0 );
+	* // returns 0.5
+	*
+	* @example
+	* var y = cdf( 2.0, -1.0, 0.5 );
+	* // returns NaN
+	*
+	* @example
+	* var y = cdf( 2.0, 0.5, -1.0 );
+	* // returns NaN
+	*
+	* @example
+	* var y = cdf( NaN, 1.0, 1.0 );
+	* // returns NaN
+	*
+	* @example
+	* var y = cdf( 0.0, NaN, 1.0 );
+	* // returns NaN
+	*
+	* @example
+	* var y = cdf( 0.0, 1.0, NaN );
+	* // returns NaN
+	*/
+	( x: number, alpha: number, beta: number ): number;
+
+	/**
+	* Returns a function for evaluating the cumulative distribution function (CDF) for a Burr (type III) distribution with first shape parameter `alpha` and second shape parameter `beta`.
+	*
+	* @param alpha - first shape parameter
+	* @param beta - second shape parameter
+	* @returns CDF
+	*
+	* @example
+	* var myCDF = cdf.factory( 0.5, 0.5 );
+	*
+	* var y = myCDF( 0.8 );
+	* // returns ~0.69
+	*
+	* y = myCDF( 0.3 );
+	* // returns ~0.59
+	*/
+	factory( alpha: number, beta: number ): Unary;
+}
+
+/**
+* Burr (type III) distribution cumulative distribution function (CDF).
+*
+* @param x - input value
+* @param alpha - first shape parameter
+* @param beta - second shape parameter
+* @returns evaluated CDF
+*
+* @example
+* var y = cdf( 0.5, 1.0, 1.0 );
+* // returns ~0.33
+*
+* y = cdf( 0.5, 2.0, 4.0 );
+* // returns ~0.0015
+*
+* var myCDF = cdf.factory( 0.5, 0.5 );
+*
+* y = myCDF( 0.8 );
+* // returns ~0.69
+*
+* y = myCDF( 0.3 );
+* // returns ~0.59
+*/
+declare var cdf: CDF;
+
+
+// EXPORTS //
+
+export = cdf;