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@stdlib/stats

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Standard library statistical functions.

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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 betaln = require( '@stdlib/math/base/special/betaln' ); var sqrt = require( '@stdlib/math/base/special/sqrt' ); var pow = require( '@stdlib/math/base/special/pow' ); var ln = require( '@stdlib/math/base/special/ln' ); // MAIN // /** * Evaluates the natural logarithm of the probability density function (PDF) for a Student's t distribution with degrees of freedom `v` at a value `x`. * * @param {number} x - input value * @param {PositiveNumber} v - degrees of freedom * @returns {number} evaluated logPDF * * @example * var y = logpdf( 0.3, 4.0 ); * // returns ~-1.036 * * @example * var y = logpdf( 2.0, 0.7 ); * // returns ~-2.841 * * @example * var y = logpdf( -1.0, 0.5 ); * // returns ~-2.134 * * @example * var y = logpdf( 0.0, NaN ); * // returns NaN * * @example * var y = logpdf( NaN, 2.0 ); * // returns NaN * * @example * var y = logpdf( 2.0, -1.0 ); * // returns NaN */ function logpdf( x, v ) { var betaTerm; if ( isnan( x ) || isnan( v ) || v <= 0.0 ) { return NaN; } betaTerm = ln( sqrt( v ) ) + betaln( v/2.0, 0.5 ); return ( ( (1.0+v) / 2.0 ) * ln( v / ( v + pow( x, 2.0 ) ) ) ) - betaTerm; } // EXPORTS // module.exports = logpdf;