Elamur Groupantsmlab-builtins-stats-distributions
The groupant beside mlab/src/builtins/stats.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| cost | symbolic source derived | invariant |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | partial bounded parent evidence | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
broadcast_shape | broadcast_shape | partial source derived model | broadcast_shape |
tail_precision | tail_precision | partial source derived model | tail_precision |
branch_relation | branch_relation | partial source derived model | branch_relation |
resource_cost | resource_cost | partial source derived model | resource_cost |
Model text
descriptant
mlab-builtins-stats-distributions
Registry installs scalar-broadcast distributions. bcast checks arity/types then identical nonscalar shape, defaults scalar parameters. phi=erfc(-z/sqrt2)/2 with infinities explicit. phi_inv uses statrs seed plus2 Newton steps. dinv linearly returns least k with CDF(k)>=p, p=1 returns kmax.
Epoch 2026-10-31: isolated source-bound fragment over bytes [907,7891); includes no claim beyond this relation. Source hash bdc3772b09d9113e108afa29e391fee97a5372caf9052bb1689996c41c94116f.
approximant
distributions: forward relation
Registry installs scalar-broadcast distributions. bcast checks arity/types then identical nonscalar shape, defaults scalar parameters. phi=erfc(-z/sqrt2)/2 with infinities explicit. phi_inv uses statrs seed plus2 Newton steps. dinv linearly returns least k with CDF(k)>=p, p=1 returns kmax.
Domain: Finite, well-shaped bounded observations unless branch explicitly describes NaN/Inf. Direct public chi2/OLS helpers assume dimensions not checked at every index; wrappers add validation.
Executable surrogate gap: no measured cheaper implementation with a useful scoped metric is supplied. Categorical/error/effect relations are exact obligations, not percent losses. Future numeric caps only1/2/5/10%.
invariant
distributions: invariant and cost
Scalar parameters broadcast to first nonscalar shape, not general singleton-axis broadcasting.
libm erfc avoids 1-erf cancellation; numerical implementation not a universal accuracy certificate.
Scope-specific cost: Broadcast O(ncells*nparams + distribution evaluation), discrete inverse O(returned k) CDF calls without bounded cap; phi_inv two Newton steps.
models
behavior_complement
Invalid p excludes finite inverse except NaN mapping; continuous unsupported parameters become NaN, not interpreter errors. Discrete p=1 can yield infinity.
reverse_reconstruction
CDF observation admits parameters and x satisfying F_theta(x)=p; discrete quantile admits interval F(k-1)<p<=F(k), endpoint conventions special.
broadcast_shape
Scalar parameters broadcast to first nonscalar shape, not general singleton-axis broadcasting.
tail_precision
libm erfc avoids 1-erf cancellation; numerical implementation not a universal accuracy certificate.
branch_relation
Registry installs scalar-broadcast distributions. bcast checks arity/types then identical nonscalar shape, defaults scalar parameters. phi=erfc(-z/sqrt2)/2 with infinities explicit. phi_inv uses statrs seed plus2 Newton steps. dinv linearly returns least k with CDF(k)>=p, p=1 returns kmax.
resource_cost
Broadcast O(ncells*nparams + distribution evaluation), discrete inverse O(returned k) CDF calls without bounded cap; phi_inv two Newton steps.
tests
Evidence boundary
See ../tests.md for the actual selected source test and mutant. These tests sample the file, not every fragment branch. Invalid p excludes finite inverse except NaN mapping; continuous unsupported parameters become NaN, not interpreter errors. Discrete p=1 can yield infinity. Other branches here are source-derived and unexecuted unless the parent test explicitly calls them.
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