time-to-botec

main.js (6055B)

---

 /**
 * @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 setReadOnly = require( '@stdlib/utils/define-read-only-property' );
 var isNumberArray = require( '@stdlib/assert/is-number-array' );
 var isNonNegativeInteger = require( '@stdlib/assert/is-nonnegative-integer' );
 var betaQuantile = require( './../../base/dists/beta/quantile' );
 var floor = require( '@stdlib/math/base/special/floor' );
 var ceil = require( '@stdlib/math/base/special/ceil' );
 var binomialCDF = require( './../../base/dists/binomial/cdf' );
 var binomialPMF = require( './../../base/dists/binomial/pmf' );
 var validate = require( './validate.js' );
 var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
 
 
 // VARIABLES //
 
 var RELATIVE_ERROR = 1+1e-07;
 
 
 // FUNCTIONS //
 
 /**
 * Calculates the lower endpoint of a confidence interval.
 *
 * @private
 * @param {NonNegativeInteger} x - number of successes
 * @param {NonNegativeInteger} n - total number of observations
 * @param {number} alpha - significance level
 * @returns {number} lower endpoint
 */
 function lower( x, n, alpha ) {
 	return ( x === 0 ) ? 0 : betaQuantile( alpha, x, n - x + 1 );
 }
 
 /**
 * Calculates the upper endpoint of a confidence interval.
 *
 * @private
 * @param {NonNegativeInteger} x - number of successes
 * @param {NonNegativeInteger} n - total number of observations
 * @param {number} alpha - significance level
 * @returns {number} upper endpoint
 */
 function upper( x, n, alpha ) {
 	return ( x === n ) ? 1 : betaQuantile( 1 - alpha, x + 1, n - x );
 }
 
 
 // MAIN //
 
 /**
 * Computes an exact test for the success probability in a Bernoulli experiment.
 *
 * @param {(NonNegativeInteger|Array)} x - number of successes or two-element array with successes and failures
 * @param {NonNegativeInteger} [n] - total number of observations
 * @param {Options} [options] - function options
 * @param {number} [options.alpha=0.05] - significance level
 * @param {string} [options.alternative='two-sided'] - alternative hypothesis (`two-sided`, `less` or `greater`)
 * @param {Probability} [options.p=0.5] - success probability under H0
 * @throws {TypeError} options has to be simple object
 * @throws {TypeError} must provide valid options
 * @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
 * @throws {TypeError} alternative option has to be a string primitive
 * @throws {Error} alternative option must be `two-sided`, `less` or `greater`
 * @returns {Object} test results
 */
 function binomialTest() {
 	var alpha;
 	var opts;
 	var cint;
 	var pval;
 	var stat;
 	var alt;
 	var err;
 	var out;
 	var d;
 	var m;
 	var n;
 	var p;
 	var x;
 	var y;
 	var i;
 
 	opts = {};
 	if ( isNumberArray( arguments[ 0 ] ) ) {
 		x = arguments[ 0 ];
 		if ( x.length !== 2 ) {
 			throw new Error( 'invalid argument. If provided an array, it must have two elements. Value: `' + x + '`.' );
 		}
 		n = x[ 1 ] + x[ 0 ];
 		x = x[ 0 ];
 		if ( arguments[ 1 ] ) {
 			err = validate( opts, arguments[ 1 ] );
 		}
 	} else {
 		x = arguments[ 0 ];
 		n = arguments[ 1 ];
 		if ( !isNonNegativeInteger( x ) ) {
 			throw new TypeError( 'invalid argument. Must provide a nonnegative integer or a two-element array. Value: `' + x + '`.' );
 		}
 		if ( !isNonNegativeInteger( n ) ) {
 			throw new TypeError( 'invalid argument. Must provide a nonnegative integer. Value: `' + n + '`.' );
 		}
 		if ( x > n ) {
 			throw new TypeError( 'invalid arguments. `x` cannot be larger than `n`. `x:' + x + ', n:' + n + '`.' );
 		}
 		if ( arguments[ 2 ] ) {
 			err = validate( opts, arguments[ 2 ] );
 		}
 	}
 	if ( err ) {
 		throw err;
 	}
 
 	if ( opts.alpha === void 0 ) {
 		alpha = 0.05;
 	} else {
 		alpha = opts.alpha;
 	}
 	if ( alpha < 0.0 || alpha > 1.0 ) {
 		throw new RangeError( 'invalid argument. Option `alpha` must be a number in the range 0 to 1. Value: `' + alpha + '`.' );
 	}
 	if ( opts.p === void 0 ) {
 		p = 0.5;
 	} else {
 		p = opts.p;
 	}
 	if ( p < 0.0 || p > 1.0 ) {
 		throw new RangeError( 'invalid argument. Option `p` must be a probability. Value: `' + p + '`.' );
 	}
 
 	alt = opts.alternative || 'two-sided';
 	stat = x / n;
 	switch ( alt ) {
 	case 'less':
 		pval = binomialCDF( x, n, p );
 		cint = [ 0.0, upper( x, n, alpha ) ];
 		break;
 	case 'greater':
 		pval = 1.0 - binomialCDF( x - 1, n, p );
 		cint = [ lower( x, n, alpha ), 1.0 ];
 		break;
 	case 'two-sided':
 		d = binomialPMF( x, n, p );
 		m = n * p;
 		if ( x === m ) {
 			pval = 1;
 		} else if ( x < m ) {
 			y = 0;
 			for ( i = ceil( m ); i <= n; i++ ) {
 				if ( binomialPMF( i, n, p ) <= d * RELATIVE_ERROR ) {
 					y += 1;
 				}
 			}
 			pval = binomialCDF(x, n, p) + ( 1 - binomialCDF(n - y, n, p ) );
 		} else {
 			y = 0;
 			for ( i = 0; i <= floor( m ); i++ ) {
 				if ( binomialPMF( i, n, p ) <= d * RELATIVE_ERROR ) {
 					y += 1;
 				}
 			}
 			pval = binomialCDF( y-1, n, p ) + ( 1 - binomialCDF( x-1, n, p ) );
 		}
 		cint = [ lower( x, n, alpha/2.0 ), upper( x, n, alpha/2.0 ) ];
 		break;
 	default:
 		throw new Error( 'Invalid option. `alternative` must be either `two-sided`, `less` or `greater`. Value: `' + alt + '`' );
 	}
 
 	out = {};
 	setReadOnly( out, 'rejected', pval <= alpha );
 	setReadOnly( out, 'alpha', alpha );
 	setReadOnly( out, 'pValue', pval );
 	setReadOnly( out, 'statistic', stat );
 	setReadOnly( out, 'ci', cint );
 	setReadOnly( out, 'nullValue', p );
 	setReadOnly( out, 'alternative', alt );
 	setReadOnly( out, 'method', 'Exact binomial test' );
 	setReadOnly( out, 'print', print );
 	return out;
 }
 
 
 // EXPORTS //
 
 module.exports = binomialTest;