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declare(strict_types=1);
namespace Dochia;
/**
* Predictive distribution with body scale and separate tail stretching.
*
* The body (between tail anchors) is a lognormal mixture; the lower and upper
* tails are stretched so that the 80% interval and the 95% interval can be
* calibrated independently. This is a coherent piecewise distribution.
*/
final class CalibratedPredictive
{
public function __construct(
public readonly LognormalMixture $base,
public readonly float $anchorLow,
public readonly float $anchorHigh,
public readonly float $scaleLow,
public readonly float $scaleHigh,
public readonly float $qLow,
public readonly float $qHigh,
) {
}
public static function fromBase(LognormalMixture $base, ModelParams $params): self
{
return new self(
base: $base,
anchorLow: $params->tailAnchorLow,
anchorHigh: $params->tailAnchorHigh,
scaleLow: max($params->tailScaleLow, 1e-6),
scaleHigh: max($params->tailScaleHigh, 1e-6),
qLow: $base->quantile($params->tailAnchorLow),
qHigh: $base->quantile($params->tailAnchorHigh),
);
}
public function quantile(float $p): float
{
if ($p <= 0.0) {
return 0.0;
}
if ($p >= 1.0) {
return 1000.0;
}
if ($p <= $this->anchorLow) {
return $this->qLow + ($this->base->quantile($p) - $this->qLow) * $this->scaleLow;
}
if ($p >= $this->anchorHigh) {
return $this->qHigh + ($this->base->quantile($p) - $this->qHigh) * $this->scaleHigh;
}
return $this->base->quantile($p);
}
public function cdf(float $x): float
{
if ($x <= $this->qLow) {
$y = $this->qLow + ($x - $this->qLow) / $this->scaleLow;
return min(max($this->base->cdf($y), 0.0), 1.0);
}
if ($x >= $this->qHigh) {
$y = $this->qHigh + ($x - $this->qHigh) / $this->scaleHigh;
return min(max($this->base->cdf($y), 0.0), 1.0);
}
return $this->base->cdf($x);
}
public function pdf(float $x): float
{
if ($x <= 0.0) {
return 0.0;
}
if ($x < $this->qLow) {
return $this->base->pdf($this->qLow + ($x - $this->qLow) / $this->scaleLow) / $this->scaleLow;
}
if ($x > $this->qHigh) {
return $this->base->pdf($this->qHigh + ($x - $this->qHigh) / $this->scaleHigh) / $this->scaleHigh;
}
return $this->base->pdf($x);
}
public function mean(): float
{
return $this->base->mean;
}
public function sd(): float
{
return $this->base->sd;
}
}
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