var $n;

var $mean;

var $percentile;

var $probability;

var $df;

var $reference;

var $X = array();

var $Y = array();

//Function to calculate arithmetic average

function average($X){

if (!count($X)) return 0;

$sum = 0;

for ($i = 0; $i < count($X); $i++)

{

$sum += $X[$i];

}

return $sum / count($X);

}

// Function to calculate standard deviation (n-1)

function sd($X) {

if (count($X)<2) return 0;

$aver=$this->average($X);

$sum = 0;

for ($i = 0; $i < count($X); $i++)

{

$sum += ($X[$i]-$aver)*($X[$i]-$aver);

}

return sqrt($sum / (count($X)-1));

}

//Function to calculate percentiles

function mypercentile($X,$percentile){

if( 0 < $percentile && $percentile < 1 ) {

$p = $percentile;

}else if( 1 < $percentile && $percentile <= 100 ) {

$p = $percentile * .01;

}else {

return "";

}

$count = count($X);

$allindex = ($count-1)*$p;

$intvalindex = intval($allindex);

$floatval = $allindex - $intvalindex;

sort($X);

if(!is_float($floatval)){

$result = $X[$intvalindex];

}else {

if($count > $intvalindex+1)

$result = $floatval*($X[$intvalindex+1] - $X[$intvalindex]) + $X[$intvalindex];

else

$result = $X[$intvalindex];

}

return $result;

}

//Function to calculate Scaled median absolute deviation (MAD).

function mad($X){

if (!count($X)) return 0;

$median = $this->mypercentile($X,50);

if (count($X)<10){

$sum = 0;

for ($i = 0; $i < count($X); $i++)

{

$sum += abs($X[$i]-$median);

}

$result =(1/(0.798*count($X)))*$sum;

return $result;

}else{

for ($i = 0; $i < count($X); $i++)

{

$medi[]= abs($X[$i]-$median);

}

$med=$this->mypercentile($medi,50);

$result =1.483*$med;

return $result;

}

}

//Function to calculate relative standard deviation (RSD). Coefficient of variation is 100*RSD.

function rsd($X){

$result =($this->sd($X))/($this->average($X));

return $result;

}

//Function to calculate relative standard deviation (RSD) with robust estimators. Coefficient of variation is 100*RSD.

function rsdrob($X){

$result =($this->mad($X))/($this->mypercentile($X,50));

return $result;

}

//Function to calculate percentage of root mean square (RMS) for a reference value (CRM, recovery,...).

function rms($X,$reference){

$sesgo=0;

for($i=0;$i<count($X);$i++){

$sesgo+=($X[$i]-$reference)*($X[$i]-$reference);

}

$raiz=sqrt($sesgo / count($X));

return $raiz;

}

//Function for F and t distributions

function doCommonMath($q, $i, $j, $b) {

$zz = 1;

$z = $zz;

$k = $i;

while($k <= $j) {

$zz = $zz * $q * $k / ($k - $b);

$z = $z + $zz;

$k = $k + 2;

}

return $z;

}

//Function to calculate the value of the distribution F

function getFisherF($f, $n1, $n2) {

$x = $n2 / ($n1 * $f + $n2);

if(($n1%2)==0) {

return $this->doCommonMath(1-$x, $n2, $n1+$n2-4, $n2-2) * pow($x, $n2/2);

}

if(($n2%2)==0){

return 1 - $this->doCommonMath($x, $n1, $n1+$n2-4, $n1-2) * pow(1-$x, $n1/2);

}

$th = atan(sqrt($n1 * $f / $n2));

$a = $th / (pi() / 2);

$sth = sin($th);

$cth = cos($th);

if($n2 > 1) {

$a = $a + $sth * $cth * $this->doCommonMath($cth*$cth, 2, $n2-3, -1) / (pi()/2);

}

if($n1==1) {

return 1 - $a;

}

$c = 4 * $this->doCommonMath($sth*$sth, $n2+1, $n1+$n2-4, $n2-2)* $sth * pow($cth,$n2) / pi();

if($n2==1) {

return 1 - $a + $c/2;

}

$k=2;

while($k<=($n2-1)/2) {

$c = $c * $k/($k-.5);

$k=$k+1;

}

return 1-$a+$c;

}

//Function to calculate the inverse value of the distribution F

function getInverseFisherF($probability, $X, $Y) {

if( 0 < $probability && $probability < 1 ) {

$p = $probability;

}else {

$p = (100-$probability) * 0.01;

}

$n1=count($X)-1;

$n2=count($Y)-1;

$v = 0.5;

$dv = 0.5;

$f = 0.0;

while($dv > 1e-10) {

$f = (1 / $v) - 1;

$dv = $dv / 2;

if($this->getFisherF($f, $n1, $n2) > $p) {

$v = $v - $dv;

} else {

$v = $v + $dv;

}

}

return $f;

}

//Function to calculate the value of the distribution t-student

function getStudentT($t, $df) {

$t = abs($t);

$w = $t / sqrt($df);

$th = atan($w);

if ($df == 1) {

return 1 - $th / (pi() / 2);

}

$sth = sin($th);

$cth = cos($th);

if( ($df % 2) ==1 ) {

return 1 - ($th + $sth * $cth * $this->doCommonMath($cth * $cth, 2, $df - 3, -1)) / (pi()/2);

} else {

return 1 - $sth * $this->doCommonMath($cth * $cth, 1, $df - 3, -1);

}

}

//Function to calculate the inverse value of the distribution t-student

function getInverseStudentT($probability, $X) {

if( 0 < $probability && $probability < 1 ) {

$p = $probability;

}else {

$p = (100-$probability) * 0.01;

}

$df=count($X)-1;

$v = 0.5;

$dv = 0.5;

$t = 0;

while($dv > 1e-6) {

$t = (1 / $v) - 1;

$dv = $dv / 2;

if ( $this->getStudentT($t, $df) > $p) {

$v = $v - $dv;

} else {

$v = $v + $dv;

}

}

return $t;

}

//Function to calculate the value of F for two populations

function getFcalc($X, $Y) {

$variancex=$this->sd($X)*$this->sd($X);

$variancey=$this->sd($Y)*$this->sd($Y);

$maxim=max($variancex,$variancey);

$minim=min($variancex,$variancey);

$fcalc=$maxim/$minim;

return $fcalc;

}

//Function to calculate the value of t for a reference value (CRM, recovery..)

function getTcalc($X, $reference) {

$avervalues=$this->average($X);

$sdvalues=$this->sd($X);

$n=count($X);

$tcalc=(abs($avervalues-$reference)*sqrt($n))/$sdvalues;

return $tcalc;

}

/*Estimation of measurement relative uncertainty based in the following assumptions:

- The data $X are in reproducibility conditions (RSD). The laboratory not analyzed in repeatability conditions.

- The outlier datas are identified and removed.

- The reference value is the theorical value or 100 for recovery data.

- RMS is the only one estimation for the bias of the measurement.

- Coberture factor is the t-student value for a 95% of probability.

*/

function uncertainty($X,$reference) {

$median=$this->mypercentile($X,50);

$mad=$this->mad($X);

$outliermax=$median+3*$mad;

$outliermin=$median-3*$mad;

for ($i = 0; $i < count($X); $i++)

{

if( $X[$i]> $outliermin & $X[$i]< $outliermax ){

$Z[] = $X[$i];

}

}

$reprod=$this->rsd($Z);

$bias=$this->rms($Z,$reference);

$df=count($Z)-1;

$coberture=$this->getInverseStudentT(95,$Z);

$uncert=100*($coberture*sqrt($reprod*$reprod+$bias*$bias));

return $uncert;

}

//Function to formats a number ($value) to a specified number of significant figures.

function sigFig($value, $sigFigs) {

$exponent = floor(log10(abs($value))+1);

$significand = round(($value

/ pow(10, $exponent))

* pow(10, $sigFigs))

/ pow(10, $sigFigs);

return $significand * pow(10, $exponent);

}