Moment-Generating Function
Exponential distribution moment-generating function (MGF).
The moment-generating function for an exponential random variable is
where lambda > 0
is the rate parameter. For t >= lambda
, the MGF is undefined and this module returns NaN
.
Installation
$ npm install distributions-exponential-mgf
For use in the browser, use browserify.
Usage
var mgf = ;
mgf( t[, options] )
Evaluates the moment-generating function (MGF) for the exponential distribution. t
may be either a number
, an array
, a typed array
, or a matrix
.
var matrix =matoutti;out = ;// returns 2out = ;// returns 0.5t = 0 02 04 06 08 1 ;out = ;// returns [ 1, 1.25, ~1.667, 2.5, 5, NaN ]t = t ;out = ;// returns Float64Array( [1,1.25,~1.667,2.5,5,NaN] )t = 6 ;for i = 0; i < 6; i++t i = i * 02;mat = ;/*[ 0 0.20.4 0.60.8 1 ]*/out = ;/*[ 1 1.25~1.667 2.55 NaN ]*/
The function accepts the following options
:
- lambda: rate parameter. Default:
1
. - accessor: accessor
function
for accessingarray
values. - dtype: output
typed array
ormatrix
data type. Default:float64
. - copy:
boolean
indicating if thefunction
should return a new data structure. Default:true
. - path: deepget/deepset key path.
- sep: deepget/deepset key path separator. Default:
'.'
.
An exponential distribution is a function of one parameter: lambda > 0
(rate parameter). By default, lambda
is equal to 1
. To adjust either parameter, set the corresponding option.
var t = 0 05 1 15 2 25 ;var out =;// returns [ 1, ~1.143, ~1.333, 1.6, 2, ~2.667 ]
For non-numeric arrays
, provide an accessor function
for accessing array
values.
var data =001052131542525;{return d 1 ;}var out =;// returns [ 1, ~1.143, ~1.333, 1.6, 2, ~2.667 ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
var data ='x':00'x':105'x':21'x':315'x':42'x':525;var out =;/*[{'x':[0,1]},{'x':[1,~1.143]},{'x':[2,~1.333]},{'x':[3,1.6]},{'x':[4,2]},{'x':[5,~2.667]}]*/var bool = data === out ;// returns true
By default, when provided a typed array
or matrix
, the output data structure is float64
in order to preserve precision. To specify a different data type, set the dtype
option (see matrix
for a list of acceptable data types).
var t out;t = 01234 ;out =;// returns Int32Array( [1,1,1,2,5] )// Works for plain arrays, as well...out =;// returns Uint8Array( [1,1,1,2,5] )
By default, the function returns a new data structure. To mutate the input data structure (e.g., when input values can be discarded or when optimizing memory usage), set the copy
option to false
.
var boolmatoutti;t = 0 02 04 06 08 1 ;out =;// returns [ 1, 1.25, ~1.667, 2.5, 5, NaN ]bool = t === out ;// returns truet = 6 ;for i = 0; i < 6; i++t i = i * 02;mat = ;/*[ 0 0.20.4 0.60.8 1 ]*/out =;/*[ 1 1.25~1.667 2.55 NaN ]*/bool = mat === out ;// returns true
Notes
-
If an element is not a numeric value, the evaluated MGF is
NaN
.var data out;out = ;// returns NaNout = ;// returns NaNout = ;// returns NaNout = ;// returns [ NaN, NaN, NaN ]{return dx;}data ='x':true'x':'x':{}'x':null;out =;// returns [ NaN, NaN, NaN, NaN ]out =;/*[{'x':NaN},{'x':NaN},{'x':NaN,{'x':NaN}]*/ -
Be careful when providing a data structure which contains non-numeric elements and specifying an
integer
output data type, asNaN
values are cast to0
.var out =;// returns Int8Array( [0,0,0] );
Examples
var mgf =matrix = ;var datamatouttmpi;// Plain arrays...data = 10 ;for i = 0; i < datalength; i++data i = i * 01;out = ;// Object arrays (accessors)...{return dx;}for i = 0; i < datalength; i++data i ='x': data i;out =;// Deep set arrays...for i = 0; i < datalength; i++data i ='x': i data i x;out =;// Typed arrays...data = 10 ;for i = 0; i < datalength; i++data i = i * 01;out = ;// Matrices...mat = ;out = ;// Matrices (custom output data type)...out =;
To run the example code from the top-level application directory,
$ node ./examples/index.js
Tests
Unit
Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:
$ make test
All new feature development should have corresponding unit tests to validate correct functionality.
Test Coverage
This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:
$ make test-cov
Istanbul creates a ./reports/coverage
directory. To access an HTML version of the report,
$ make view-cov
License
Copyright
Copyright © 2015. The Compute.io Authors.