README.md

Mode

Erlang distribution mode.

The mode for an Erlang random variable is

$$\mathop{\mathrm{mode}}\left( X \right) = \frac{1}{\lambda}(k - 1)$$

where k is the shape parameter and λ is the rate parameter.

Usage

var mode = require( '@stdlib/stats/base/dists/erlang/mode' );

mode( k, lambda )

Returns the mode of an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

var v = mode( 1, 1.0 );
// returns 0.0

v = mode( 4, 12.0 );
// returns 0.25

v = mode( 8, 2.0 );
// returns 3.5

If provided NaN as any argument, the function returns NaN.

var v = mode( NaN, 2.0 );
// returns NaN

v = mode( 2.0, NaN );
// returns NaN

If not provided a positive integer for k, the function returns NaN.

var v = mode( 1.8, 1.0 );
// returns NaN

v = mode( -1.0, 1.0 );
// returns NaN

If provided lambda <= 0, the function returns NaN.

var v = mode( 2, 0.0 );
// returns NaN

v = mode( 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 mode = require( '@stdlib/stats/base/dists/erlang/mode' );

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 = mode( k, lambda );
    console.log( 'k: %d, λ: %d, mode(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}

---

C APIs

Usage

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

stdlib_base_dists_erlang_mode( k, lambda )

Returns the mode of an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

double out = stdlib_base_dists_erlang_mode( 1, 1.0 );
// returns 0.0

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/erlang/mode.h"
#include "stdlib/math/base/special/round.h"
#include "stdlib/constants/float64/eps.h"
#include <stdint.h>
#include <stdlib.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_mode( k, lambda );
        printf( "k: %d, λ: %lf, mode(X;k,λ): %lf\n", k, lambda, y );
    }
}