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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 constantFunction = require( '@stdlib/utils/constant-function' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pow = require( '@stdlib/math/base/special/pow' );
var log1mexp = require( '@stdlib/math/base/special/log1mexp' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var expm1 = require( '@stdlib/math/base/special/expm1' );
var ln = require( '@stdlib/math/base/special/ln' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' );
// MAIN //
/**
* Returns a function for evaluating the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution with first shape parameter `a` and second shape parameter `b`.
*
* @param {PositiveNumber} a - first shape parameter
* @param {PositiveNumber} b - second shape parameter
* @returns {Function} CDF
*
* @example
* var logcdf = factory( 0.5, 0.5 );
*
* var y = logcdf( 0.8 );
* // returns ~-0.393
*
* y = logcdf( 0.3 );
* // returns ~-1.116
*/
function factory( a, b ) {
if (
isnan( a ) ||
isnan( b ) ||
a <= 0.0 ||
b <= 0.0
) {
return constantFunction( NaN );
}
return logcdf;
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 2.0 );
* // returns <number>
*/
function logcdf( x ) {
var u;
var v;
var t;
if ( isnan( x ) ) {
return NaN;
}
if ( x <= 0.0 ) {
return NINF;
}
if ( x >= 1.0 ) {
return 0.0;
}
// Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself:
u = pow( x, a );
if ( u < FLOAT64_SMALLEST_NORMAL ) {
// `x^a` is subnormal or underflows, so `ln(1-(1-x^a)^b) = ln(b) + a*ln(x)`:
return ln( b ) + ( a * ln( x ) );
}
if ( u < 0.5 ) {
v = log1p( -u );
} else {
v = ln( -expm1( a * ln( x ) ) );
}
t = b * v;
if ( t > -FLOAT64_SMALLEST_NORMAL ) {
return ln( b ) + ln( -v );
}
return log1mexp( t );
}
}
// EXPORTS //
module.exports = factory;
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