Mean
Erlang distribution expected value.
The mean for an Erlang random variable is
where k
is the shape parameter and λ
is the rate parameter.
Usage
var mean = require( '@stdlib/stats/base/dists/erlang/mean' );
mean( k, lambda )
Returns the expected value of an Erlang distribution with parameters k
(shape parameter) and lambda
(rate parameter).
var v = mean( 1, 1.0 );
// returns 1.0
v = mean( 4, 12.0 );
// returns ~0.333
v = mean( 8, 2.0 );
// returns 4.0
If provided NaN
as any argument, the function returns NaN
.
var v = mean( NaN, 2.0 );
// returns NaN
v = mean( 2.0, NaN );
// returns NaN
If not provided a positive integer for k
, the function returns NaN
.
var v = mean( 1.8, 1.0 );
// returns NaN
v = mean( -1.0, 1.0 );
// returns NaN
If provided lambda <= 0
, the function returns NaN
.
var v = mean( 2, 0.0 );
// returns NaN
v = mean( 2, -1.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var EPS = require( '@stdlib/constants/float64/eps' );
var mean = require( '@stdlib/stats/base/dists/erlang/mean' );
var lambda;
var k;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
k = round( randu()*10.0 );
lambda = ( randu()*10.0 ) + EPS;
v = mean( k, lambda );
console.log( 'k: %d, λ: %d, E(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}