Distributions (R)

hecfda’s C++ core ports all 13 distribution families from HEC.FDA.Statistics. Every family is addressed the same way: a name string and a numeric parameter vector, in the order the core factory expects (the same order the fixtures/distributions/*.json oracle files use). One generic set of functions covers all of them: dist_pdf(), dist_cdf(), dist_quantile(), and dist_sample().

Nine families are reachable this way, through the generic factory dispatch:

Family	Name string	Parameter order	Notes
Normal	`"Normal"`	`mean, sd, sample_size`
Uniform	`"Uniform"`	`min, max, sample_size`
Triangular	`"Triangular"`	`min, most_likely, max, sample_size`
Deterministic	`"Deterministic"`	`value`	a point mass
LogNormal	`"LogNormal"`	`mean, sd, sample_size`	moments of the natural-log-scale data
TruncatedNormal	`"TruncatedNormal"`	`mean, sd, min, max, sample_size`
TruncatedLogNormal	`"TruncatedLogNormal"`	`mean, sd, min, max, sample_size`	moments of the natural-log-scale data
LogPearsonIII	`"LogPearsonIII"`	`mean, sd, skew, sample_size`	moments of the log10-scale data; the flood-frequency workhorse
TruncatedLogPearson3	`"TruncatedLogPearson3"`	`mean, sd, skew, min, max, sample_size`	moments of the log10-scale data

Four of the 13 families are not on this list, and calling dist_pdf() with any of their names raises an error rather than constructing one. Gamma, ShiftedGamma, and PearsonIII are internal helper classes in the C++ core, not members of the IDistribution factory, so they have no name string at all. Empirical is a full IDistribution member, but is not constructible by name through the factory: it is built from data (a histogram or a set of quantiles), not from a short parameter vector, so it has its own construction path rather than a dist_pdf()-style entry point. See the porting status page for where each of these lives.

Density, CDF, and quantile

Two families illustrate the range hecfda covers: Normal, a light-tailed, symmetric distribution, and LogPearsonIII, the heavy-tailed flood-frequency distribution HEC-FDA uses for annual peak flows. Both plots below evaluate dist_pdf(), dist_cdf(), and dist_quantile() over a grid and draw the three curves in the same earth-tone palette used throughout these examples.

x = seq(-4, 4, length.out = 200)
p = seq(0.001, 0.999, length.out = 200)
params = c(0, 1, 1)

par(mfrow = c(1, 3))
plot(x, dist_pdf("Normal", params, x), type = "l", col = "#6b705c", lwd = 2,
     xlab = "x", ylab = "density", main = "pdf")
plot(x, dist_cdf("Normal", params, x), type = "l", col = "#a5a58d", lwd = 2,
     xlab = "x", ylab = "probability", main = "cdf")
plot(p, dist_quantile("Normal", params, p), type = "l", col = "#cb997e", lwd = 2,
     xlab = "probability", ylab = "x", main = "quantile")

x = seq(100, 12000, length.out = 200)
p = seq(0.01, 0.99, length.out = 200)
params = c(3.3, 0.254, 0.0925, 99)

par(mfrow = c(1, 3))
plot(x, dist_pdf("LogPearsonIII", params, x), type = "l", col = "#6b705c", lwd = 2,
     xlab = "x", ylab = "density", main = "pdf")
plot(x, dist_cdf("LogPearsonIII", params, x), type = "l", col = "#a5a58d", lwd = 2,
     xlab = "x", ylab = "probability", main = "cdf")
plot(p, dist_quantile("LogPearsonIII", params, p), type = "l", col = "#cb997e", lwd = 2,
     xlab = "probability", ylab = "x", main = "quantile")

LogPearsonIII(mean = 3.3, sd = 0.254, skew = 0.0925, sample_size = 99)

Seeded sampling

dist_sample() draws n values by applying the seeded generator’s uniform stream through inverse_cdf(), the same path every Monte Carlo compute in hecfda uses. A histogram of 1000 seeded Normal draws should track the analytic density closely:

draws = dist_sample("Normal", c(0, 1, 1), n = 1000L, seed = 12345L)
hist(draws, breaks = 30, freq = FALSE, col = "#a5a58d", border = "white",
     xlab = "x", main = "")
x = seq(-4, 4, length.out = 200)
lines(x, dist_pdf("Normal", c(0, 1, 1), x), col = "#588157", lwd = 2)

1000 seeded draws from Normal(0, 1) against the analytic pdf

fda.dist_sample("Normal", [0, 1, 1], n=1000, seed=12345) in Python draws the identical 1000 values, in the identical order, because both languages call the same seeded C++ generator.

Faithful bugs

Warning

This port reproduces upstream HEC-FDA behavior exactly, including a few known quirks in the C# source. Two examples that affect distributions:

Empirical’s pdf returns 0 for any x that is not an exact grid point in its data, rather than interpolating between points.
LogNormal mixes natural-log (ln) and log10 semantics inconsistently between its methods, matching the same inconsistency in the C# source rather than normalizing it.

These are not bugs in the port; they are the upstream behavior, transcribed on purpose so results match HEC-FDA exactly. The porting status page describes what is ported and what was left out.