wink-statistics
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Fast and Numerically Stable Statistical Analysis Utilities
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JavaScript
// wink-statistics
// Fast and Numerically Stable Statistical Analysis Utilities.
//
// Copyright (C) GRAYPE Systems Private Limited
//
// This file is part of “wink-statistics”.
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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// DEALINGS IN THE SOFTWARE.
// ## probability
// ### range4CI
/**
*
* Computes probability from the **observed** count of successes (`successCount`) out of the total count (`totalCount`)
* along with its **range** for required level of Confidence Interval (CI) i.e. `zscore` .
* The range is the minimum and maximum probability values for given `zscore` or CI.
*
* These computations are based on approach specified in the Wilson's *Notes on
* Probable Inference, The Law of Succession, and Statistical Inference*
* published in ASA's Journal.
*
* For quick reference, typical value of `zscore` for 90% and 95% CI is approximately
* 1.645 and 1.960 respectively.
*
* @memberof probability
* @param {number} successCount observed count of successes out of
* @param {number} totalCount the total count.
* @param {number} [zscore=1.645] for the required level of CI.
* @return {object} containing `probability`, `min` and `max`.
* @example
* range4CI( 1, 10 );
* // returns {
* // probability: 0.18518871952479238,
* // min: 0.02263232984000629,
* // max: 0.34774510920957846
* // }
* range4CI( 10, 100 );
* // returns {
* // probability: 0.1105389143431459,
* // min: 0.06071598345043355,
* // max: 0.16036184523585828
* // }
*/
var range4CI = function ( successCount, totalCount, zscore ) {
if ( ( typeof successCount !== 'number' ) || ( successCount <= 0 ) ) {
throw Error( 'probability-range4CI: successCount should be a number > 0, instead found: ' + JSON.stringify( successCount ) );
}
if ( ( typeof totalCount !== 'number' ) || ( totalCount <= 0 ) ) {
throw Error( 'probability-range4CI: totalCount should be a number > 0, instead found: ' + JSON.stringify( totalCount ) );
}
if ( totalCount < successCount ) {
throw Error( 'probability-range4CI: totalCount should be >= successCount, instead found: ' + JSON.stringify( totalCount ) );
}
var z = Math.abs( zscore || 1.645 );
var t = ( z * z ) / totalCount;
var p0 = successCount / totalCount;
var q0 = 1 - p0;
var delta = Math.sqrt( ( p0 * q0 * t ) + ( ( t * t ) / 4 ) );
var min = ( p0 + ( t / 2 ) - delta ) / ( t + 1 );
var max = ( p0 + ( t / 2 ) + delta ) / ( t + 1 );
return {
probability: ( p0 + ( t / 2 ) ) / ( t + 1 ),
min: min,
max: max
};
}; // range4CI()
module.exports = range4CI;