mir-rework.d

/+dub.sdl:
dependency "mir-random" path="./"
+/
import mir.math.common;
import mir.ndslice.sorting;
import mir.random;
import mir.random.algorithm;
import mir.random.variable;

enum n = 30; // sample size
enum numTrials = 5_000;
enum double scale = 1;
enum double lambda = 1 / scale;

// quantile [0, 1) or [0, 1]
auto orderStat(double quantile)
{
    auto r = cast(int) (quantile * n); //trunc down
    if (r == n) r = n - 1;
    return r;
}

auto cdf(double x)
{
    // trivial for uniform(0, 1)
    // return x;

    // for exponential:
    return 1-(exp(lambda * -x));
}

void main()
{
    import std.stdio;

    auto quantileFile = File("quantile.txt", "w");
    auto quantileDiffFile = File("quantile-diff.txt", "w");

    foreach(trialNum; 0 .. numTrials)
    {
        // auto sample = uniformVar(0.0, 1.0).randomSlice(n).field.sort;
        auto sample = exponentialVar(scale).randomSlice(n).field.sort;
        auto requestedQuantile = rand!double.fabs; // [0, 1)
        auto k = orderStat(requestedQuantile);
        auto estimatedQuantileValue = sample[k];
        auto trueQuantile = cdf(estimatedQuantileValue);

        quantileFile.writefln("%s %s", requestedQuantile, trueQuantile);
        quantileDiffFile.writefln("%s %s", requestedQuantile,
            trueQuantile - requestedQuantile);
    }
}