Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 4019x 4019x 4019x 4019x 4019x 4019x 4019x 4019x 4019x 4019x 4019x 4009x 4019x 12x 12x 4019x 72x 72x 4019x 1x 1x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3934x 3936x 3936x 3936x 3936x 3936x 3936x 3x 3x 3936x 1x 1x 3936x 1x 1x 3931x 3936x 1963x 3936x 1968x 1968x 3931x 3931x 3931x 3931x 3931x 3936x 3644x 3644x 287x 3936x 4019x 3x 3x 3x 3x 3x | /**
* @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 isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' );
var constantFunction = require( '@stdlib/utils/constant-function' );
var degenerate = require( '@stdlib/stats/base/dists/degenerate/quantile' ).factory;
var erfcinv = require( '@stdlib/math/base/special/erfcinv' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var round = require( '@stdlib/math/base/special/round' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var cdf = require( '@stdlib/stats/base/dists/binomial/cdf' );
var SQRT2 = require( '@stdlib/constants/float64/sqrt-two' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var searchLeft = require( './search_left.js' );
var searchRight = require( './search_right.js' );
// MAIN //
/**
* Returns a function for evaluating the quantile function for a binomial distribution with number of trials `n` and success probability `p`.
*
* @param {NonNegativeInteger} n - number of trials
* @param {Probability} p - success probability
* @returns {Function} quantile function
*
* @example
* var quantile = factory( 10, 0.5 );
* var y = quantile( 0.1 );
* // returns 3
*
* y = quantile( 0.9 );
* // returns 7
*/
function factory( n, p ) {
var sigmaInv;
var sigma;
var mu;
if (
isnan( n ) ||
isnan( p ) ||
!isNonNegativeInteger( n ) ||
n === PINF ||
p < 0.0 ||
p > 1.0
) {
return constantFunction( NaN );
}
if ( p === 0.0 || n === 0.0 ) {
return degenerate( 0.0 );
}
if ( p === 1.0 ) {
return degenerate( n );
}
mu = n * p;
sigma = sqrt( n * p * ( 1.0-p ) );
sigmaInv = 1.0 / sigma;
return quantile;
/**
* Evaluates the quantile function for a binomial distribution.
*
* @private
* @param {Probability} r - input value
* @returns {NonNegativeInteger} evaluated quantile function
*
* @example
* var y = quantile( 0.3 );
* // returns <number>
*/
function quantile( r ) {
var guess;
var corr;
var x2;
var x;
if ( isnan( r ) || r < 0.0 || r > 1.0 ) {
return NaN;
}
if ( r === 0.0 ) {
return 0;
}
if ( r === 1.0 ) {
return n;
}
// Cornish-Fisher expansion:
if ( r < 0.5 ) {
x = -erfcinv( 2.0 * r ) * SQRT2;
} else {
x = erfcinv( 2.0 * ( 1.0-r ) ) * SQRT2;
}
x2 = x * x;
// Skewness correction:
corr = x + ( sigmaInv * ( x2-1.0 ) / 6.0 );
guess = round( mu + (sigma * corr) );
if ( cdf( guess, n, p ) >= r ) {
return searchLeft( guess, r, n, p );
}
return searchRight( guess, r, n, p );
}
}
// EXPORTS //
module.exports = factory;
|