Compute the mean percentage error (MPE) incrementally.

The mean percentage error is defined as

upper M upper P upper E equals StartFraction 100 Over n EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts StartFraction a Subscript i Baseline minus f Subscript i Baseline Over a Subscript i Baseline EndFraction

where f_i is the forecast value and a_i is the actual value.


var incrmpe = require( '@stdlib/stats/incr/mpe' );


Returns an accumulator function which incrementally computes the mean percentage error.

var accumulator = incrmpe();

accumulator( [f, a] )

If provided input values f and a, the accumulator function returns an updated mean percentage error. If not provided input values f and a, the accumulator function returns the current mean percentage error.

var accumulator = incrmpe();

var m = accumulator( 2.0, 3.0 );
// returns ~33.33

m = accumulator( 1.0, 4.0 );
// returns ~54.17

m = accumulator( 3.0, 5.0 );
// returns ~49.44

m = accumulator();
// returns ~49.44


  • Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
  • Be careful when interpreting the mean percentage error as errors can cancel. This stated, that errors can cancel makes the mean percentage error suitable for measuring the bias in forecasts.
  • Warning: the mean percentage error is not suitable for intermittent demand patterns (i.e., when a_i is 0). Interpretation is most straightforward when actual and forecast values are positive valued (e.g., number of widgets sold).


var randu = require( '@stdlib/random/base/randu' );
var incrmpe = require( '@stdlib/stats/incr/mpe' );

var accumulator;
var v1;
var v2;
var i;

// Initialize an accumulator:
accumulator = incrmpe();

// For each simulated datum, update the mean percentage error...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) + 50.0;
    v2 = ( randu()*100.0 ) + 50.0;
    accumulator( v1, v2 );
console.log( accumulator() );
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