在PHP中实现ERF功能

Question

I want to implement an ERF function in PHP. I got its formula from wikipedia

P_Value = 1-  (  ERF ( ABS ( Residual –mean ) )/(√2*SD )

I didn't get the idea how to implement it in PHP.

Answer 1

Based on the formula you provided, only the ERF (Error function) part should look like this:

function ERF ($difference) {
    return abs($difference);
}

Now call $value = ERF($residual - $mean); from anywhere inside a php script to store the ERF value in the $value variable.

Edit: Let's assume you meant this formula:

So, it should be:

function ERF ($ll, $ul, $t, $dt, $dx) {
     $val = 0;
     for($i = $ll; $i <= $ul; $i+=$dx){
          $val +=  exp(-pow($t,2)) * $dt;
     }
     return (2/sqrt(pi())) * $val;
}

now call, $value = ERF(0, $x, $t, $dt, $dx); where $x is the upper limit, $t is the time and $dt is the dt part of integration as in time interval.

Note: I've added another parameter $dx here because it is an integral for continuous domain and $dx, $dt both should be very close to 0 for better approximations. For discrete values, you can provide both $dx and $dt as 1. And that would rather be called summation than integral.

For better approximation on integration, see Numerical integration algorithms and techniques.