logpmf.js (2065B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' ); 24 var factorialln = require( '@stdlib/math/base/special/factorialln' ); 25 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 26 var ln = require( '@stdlib/math/base/special/ln' ); 27 var NINF = require( '@stdlib/constants/float64/ninf' ); 28 var PINF = require( '@stdlib/constants/float64/pinf' ); 29 30 31 // MAIN // 32 33 /** 34 * Evaluates the natural logarithm of the probability mass function (PMF) for a Poisson distribution with mean parameter `lambda` at a value `x`. 35 * 36 * @param {number} x - input value 37 * @param {NonNegativeNumber} lambda - mean parameter 38 * @returns {number} evaluated logPMF 39 * 40 * @example 41 * var y = logpmf( 4.0, 3.0 ); 42 * // returns ~-1.784 43 * 44 * @example 45 * var y = logpmf( 1.0, 3.0 ); 46 * // returns ~-1.901 47 * 48 * @example 49 * var y = logpmf( -1.0, 2.0 ); 50 * // returns -Infinity 51 * 52 * @example 53 * var y = logpmf( 0.0, NaN ); 54 * // returns NaN 55 * 56 * @example 57 * var y = logpmf( NaN, 0.5 ); 58 * // returns NaN 59 * 60 * @example 61 * // Invalid mean parameter: 62 * var y = logpmf( 2.0, -0.5 ); 63 * // returns NaN 64 */ 65 function logpmf( x, lambda ) { 66 if ( isnan( x ) || isnan( lambda ) || lambda < 0.0 ) { 67 return NaN; 68 } 69 if ( lambda === 0.0 ) { 70 return ( x === 0.0 ) ? 0.0 : NINF; 71 } 72 if ( isNonNegativeInteger( x ) && x !== PINF ) { 73 return ( x * ln( lambda ) ) - lambda - factorialln( x ); 74 } 75 return NINF; 76 } 77 78 79 // EXPORTS // 80 81 module.exports = logpmf;