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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var floor = require( '@stdlib/math/base/special/floor' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var log1mexp = require( '@stdlib/math/base/special/log1mexp' );
var pow = require( '@stdlib/math/base/special/pow' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// MAIN //
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a geometric distribution with success probability `p` at a value `x`.
*
* @param {number} x - input value
* @param {Probability} p - success probability
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 2.0, 0.5 );
* // returns ~-0.134
*
* @example
* var y = logcdf( 2.0, 0.1 );
* // returns ~-1.306
*
* @example
* var y = logcdf( -1.0, 0.5 );
* // returns -Infinity
*
* @example
* var y = logcdf( NaN, 0.5 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, NaN );
* // returns NaN
*
* @example
* // Invalid probability
* var y = logcdf( 2.0, 1.4 );
* // returns NaN
*/
function logcdf( x, p ) {
if (
isnan( x ) ||
isnan( p ) ||
p < 0.0 ||
p > 1.0
) {
return NaN;
}
if ( x < 0.0 ) {
return NINF;
}
if ( x === PINF ) {
return 0.0;
}
x = floor( x );
if ( p < 0.5 ) {
// Forming `1-p` would round away the low-order bits of `p`:
return log1mexp( ( x+1.0 ) * log1p( -p ) );
}
// `1-p` is exact for `p >= 0.5`:
return log1p( -pow( 1.0-p, x+1.0 ) );
}
// EXPORTS //
module.exports = logcdf;
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