README.md (4469B)
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 > [Raised cosine][cosine-distribution] distribution logarithm of [probability density function (PDF)][pdf]. 24 25 <section class="intro"> 26 27 The [probability density function][pdf] (PDF) for a [raised cosine][cosine-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:cosine_pdf" align="center" raw="f(x;\mu ,s)= \begin{cases} {\frac {1}{2s}}\left[1+\cos \left({\frac {x\!-\!\mu }{s}}\,\pi \right)\right] & \text{ for } \mu - s \le x \le \mu + s \\ 0 & \text{ otherwise } \end{cases}" alt="Probability density function (PDF) for a raised cosine distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="f(x;\mu ,s)= \begin{cases} {\frac {1}{2s}}\left[1+\cos \left({\frac {x\!-\!\mu }{s}}\,\pi \right)\right] & \text{ for } \mu - s \le x \le \mu + s \\ 0 & \text{ otherwise } \end{cases}" data-equation="eq:cosine_pdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/docs/img/equation_cosine_pdf.svg" alt="Probability density function (PDF) for a raised cosine distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `μ` is the location parameter and `s > 0` is the scale 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/cosine/logpdf' ); 50 ``` 51 52 #### logpdf( x, mu, s ) 53 54 Evaluates the logarithm of the [probability density function][pdf] (PDF) for a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter). 55 56 ```javascript 57 var y = logpdf( 2.0, 0.0, 3.0 ); 58 // returns ~-2.485 59 60 y = logpdf( -1.0, 2.0, 4.0 ); 61 // returns ~-3.307 62 ``` 63 64 If provided `NaN` as any argument, the function returns `NaN`. 65 66 ```javascript 67 var y = logpdf( NaN, 0.0, 1.0 ); 68 // returns NaN 69 70 y = logpdf( 0.0, NaN, 1.0 ); 71 // returns NaN 72 73 y = logpdf( 0.0, 0.0, NaN ); 74 // returns NaN 75 ``` 76 77 If provided `s < 0`, the function returns `NaN`. 78 79 ```javascript 80 var y = logpdf( 2.0, 0.0, -1.0 ); 81 // returns NaN 82 ``` 83 84 If provided `s = 0`, the function evaluates the logarithm of the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`. 85 86 ```javascript 87 var y = logpdf( 2.0, 8.0, 0.0 ); 88 // returns -Infinity 89 90 y = logpdf( 8.0, 8.0, 0.0 ); 91 // returns Infinity 92 ``` 93 94 #### logpdf.factory( mu, s ) 95 96 Returns a function for evaluating the logarithm of the [probability density function][pdf] (PDF) of a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter). 97 98 ```javascript 99 var mylogpdf = logpdf.factory( 10.0, 2.0 ); 100 101 var y = mylogpdf( 10.0 ); 102 // returns ~-0.693 103 104 y = mylogpdf( 9.0 ); 105 // returns ~-1.386 106 ``` 107 108 </section> 109 110 <!-- /.usage --> 111 112 <section class="notes"> 113 114 ## Notes 115 116 - In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow. 117 118 </section> 119 120 <!-- /.notes --> 121 122 <section class="examples"> 123 124 ## Examples 125 126 <!-- eslint no-undef: "error" --> 127 128 ```javascript 129 var randu = require( '@stdlib/random/base/randu' ); 130 var logpdf = require( '@stdlib/stats/base/dists/cosine/logpdf' ); 131 132 var mu; 133 var s; 134 var x; 135 var y; 136 var i; 137 138 for ( i = 0; i < 10; i++ ) { 139 x = randu() * 10.0; 140 mu = randu() * 10.0; 141 s = randu() * 10.0; 142 y = logpdf( x, mu, s ); 143 console.log( 'x: %d, µ: %d, s: %d, ln(f(x;µ,s)): %d', x, mu, s, y ); 144 } 145 ``` 146 147 </section> 148 149 <!-- /.examples --> 150 151 <section class="links"> 152 153 [cosine-distribution]: https://en.wikipedia.org/wiki/Raised_cosine_distribution 154 155 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 156 157 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution 158 159 </section> 160 161 <!-- /.links -->