README.md (4223B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2018 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # Logarithm of Probability Density Function 22 23 > [Gamma][gamma-distribution] distribution logarithm of probability density function (PDF). 24 25 <section class="intro"> 26 27 The [probability density function][pdf] (PDF) for a [gamma][gamma-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:gamma_pdf" align="center" raw="f(x;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha \,-\, 1} e^{- \beta x }" alt="Probability density function (PDF) for a Gamma distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="f(x;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha \,-\, 1} e^{- \beta x }" data-equation="eq:gamma_pdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/gamma/logpdf/docs/img/equation_gamma_pdf.svg" alt="Probability density function (PDF) for a Gamma distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `α > 0` is the shape parameter and `β > 0` is the rate parameter. 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var logpdf = require( '@stdlib/stats/base/dists/gamma/logpdf' ); 50 ``` 51 52 #### logpdf( x, alpha, beta ) 53 54 Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for a [gamma][gamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter). 55 56 ```javascript 57 var y = logpdf( 2.0, 0.5, 1.0 ); 58 // returns ~-2.919 59 60 y = logpdf( 0.1, 1.0, 1.0 ); 61 // returns ~-0.1 62 63 y = logpdf( -1.0, 4.0, 2.0 ); 64 // returns -Infinity 65 ``` 66 67 If provided `NaN` as any argument, the function returns `NaN`. 68 69 ```javascript 70 var y = logpdf( NaN, 1.0, 1.0 ); 71 // returns NaN 72 73 y = logpdf( 0.0, NaN, 1.0 ); 74 // returns NaN 75 76 y = logpdf( 0.0, 1.0, NaN ); 77 // returns NaN 78 ``` 79 80 If provided `alpha < 0`, the function returns `NaN`. 81 82 ```javascript 83 var y = logpdf( 2.0, -0.5, 1.0 ); 84 // returns NaN 85 ``` 86 87 If provided `alpha = 0`, the function evaluates the logarithm of the [PDF][pdf] for a [degenerate distribution][degenerate-distribution] centered at `0`. 88 89 ```javascript 90 var y = logpdf( 2.0, 0.0, 2.0 ); 91 // returns -Infinity 92 93 y = logpdf( 0.0, 0.0, 2.0 ); 94 // returns Infinity 95 ``` 96 97 If provided `beta <= 0`, the function returns `NaN`. 98 99 ```javascript 100 var y = logpdf( 2.0, 1.0, 0.0 ); 101 // returns NaN 102 103 y = logpdf( 2.0, 1.0, -1.0 ); 104 // returns NaN 105 ``` 106 107 #### logpdf.factory( alpha, beta ) 108 109 Returns a `function` for evaluating the natural logarithm of the [PDF][pdf] for a [gamma][gamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter). 110 111 ```javascript 112 var mylogpdf = logpdf.factory( 3.0, 1.5 ); 113 114 var y = mylogpdf( 1.0 ); 115 // returns ~-0.977 116 117 y = mylogpdf( 4.0 ); 118 // returns ~-2.704 119 ``` 120 121 </section> 122 123 <!-- /.usage --> 124 125 <section class="examples"> 126 127 ## Examples 128 129 <!-- eslint no-undef: "error" --> 130 131 ```javascript 132 var randu = require( '@stdlib/random/base/randu' ); 133 var logpdf = require( '@stdlib/stats/base/dists/gamma/logpdf' ); 134 135 var alpha; 136 var beta; 137 var x; 138 var y; 139 var i; 140 141 for ( i = 0; i < 10; i++ ) { 142 x = randu() * 3.0; 143 alpha = randu() * 5.0; 144 beta = randu() * 5.0; 145 y = logpdf( x, alpha, beta ); 146 console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) ); 147 } 148 ``` 149 150 </section> 151 152 <!-- /.examples --> 153 154 <section class="links"> 155 156 [gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution 157 158 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 159 160 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution 161 162 </section> 163 164 <!-- /.links -->