Exponential Cdf/Quantile lose all precision near zero: Exponential(2).Cdf(1e-17) = 0 and Quantile(1e-17) = −0 (expected 2e-17 and 5e-18) #52

What's wrong

ExponentialDistributionProvider (Essentials.DistributionProviders.Exponential/ExponentialDistributionProvider.cs) uses the cancelling forms:

• ~L53: Cdf = 1.0 - Math.Exp(-Rate * value)
• ~L72: Quantile = -Math.Log(1.0 - probability) / Rate

For small arguments the relative error is about eps/x. Below ~1e-16 the result is 0, and the quantile even comes back as negative zero, outside the support.

Repro

var e = new ExponentialDistributionProvider(2.0);
e.Cdf(1e-17);        // 0                        expected 2e-17
e.Quantile(1e-17);   // -0                       expected 5e-18
new ExponentialDistributionProvider(1.0).Cdf(1e-10); // 1.000000082740371e-10, expected 9.9999999995e-11

Why it matters

These are the textbook expm1/log1p cases. The file's own SurvivalFunction remark explains why subtracting from one rounds tails away, but the lower tail (Cdf) and Quantile don't get the same treatment. Small-probability quantiles, for example "time by which 1-in-a-billion events have happened", come out wrong or as −0.

Suggested fix

Cdf = -expm1(-Rate * x) and Quantile = -log1p(-p) / Rate, using accurate helpers. .NET's double.ExpM1/LogP1 are naive, so these belong in SpecialFunctions, shared with the Geometric fix filed alongside this issue.

Acceptance: both repro values match to ~1e-15 relative, and Quantile never returns −0.