README.md

Mean

Erlang distribution expected value.

The mean for an Erlang random variable is

$$\mathbb{E} \left[ X \right] = \frac{k}{\lambda}$$

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 ) );
}

---

C APIs

Usage

#include "stdlib/stats/base/dists/erlang/mean.h"

stdlib_base_dists_erlang_mean( k, lambda )

Evaluates the expected value of an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

double out = stdlib_base_dists_erlang_mean( 1, 1.0 );
// returns 1.0

The function accepts the following arguments:

• k: [in] int32_t shape parameter.
• lambda: [in] double rate parameter.

double stdlib_base_dists_erlang_mean( const int32_t k, const double lambda );

Examples

#include "stdlib/stats/base/dists/erlang/mean.h"
#include "stdlib/constants/float64/eps.h"
#include "stdlib/math/base/special/round.h"
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double lambda;
    int32_t k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        k = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        lambda = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_erlang_mean( k, lambda );
        printf( "k: %d, λ: %lf, E(X;k,λ): %lf\n", k, lambda, y );
    }
}