| name | applpy |
| description | Build APPLPy probability models from natural-language problem statements. Use when a request asks to translate prose into APPLPy random variables, distribution choices, composition operators (convolution, product, min/max, order statistics, mixtures, transforms, truncation), or Markov-chain/reliability constructions and return runnable Python modeling code plus key probability results. |
APPLPy Natural-Language Modeling
Overview
Translate natural-language probability modeling requests into runnable APPLPy code.
Prefer APPLPy APIs that are already exercised in repository docs and functional tests.
Workflow
- Extract the model target from the prompt.
- Identify variable type for each quantity: continuous RV, discrete RV, empirical/bootstrap RV, or Markov chain.
- Select distributions and parameters that match the described support and behavior.
- Compose derived random variables with APPLPy operators.
- Compute requested outputs with
pdf, cdf, hf, mean, variance, expected_value, quantiles via .variate(s=...), or Markov-chain methods.
- Return a complete Python snippet with imports and a short result summary.
Parse The Request
Convert prose into explicit modeling assumptions before writing code.
- Determine support and domain constraints: bounded interval, nonnegative lifetime, event counts, binary outcomes, or finite states.
- Determine if variables are independent, identically distributed, correlated, or empirical from samples.
- Determine composition intent: sums, products, minima/maxima, order statistics, mixtures, or transformed variables.
- Determine output intent: distribution form, probability query, moments, percentile, system reliability, or long-run chain behavior.
- State assumptions when input is under-specified, then choose the simplest defensible model.
Choose A Base Distribution
Use the distribution guides first.
- Discrete catalog and examples:
applpy/distributions/discrete/README.md
- Continuous catalog and examples:
applpy/distributions/continuous/README.md
Default mapping heuristics:
- Binary success/failure:
BernoulliRV(p)
- Number of successes in
N trials: BinomialRV(N, p)
- Count in interval:
PoissonRV(theta)
- Waiting time/lifetime with memoryless hazard:
ExponentialRV(theta)
- Positive skewed waiting times:
GammaRV(theta, kappa) or WeibullRV(theta, kappa)
- Bounded proportion/rate on
(0,1): BetaRV(alpha, beta)
- Symmetric measurement noise:
NormalRV(mu, sigma)
- Bounded expert estimate with mode:
TriangularRV(a, b, c)
- Finite integer range with equal mass:
UniformDiscreteRV(a, b, k=1)
- Bounded continuous range with equal density:
UniformRV(a, b)
Compose Models
Use these APPLPy construction patterns from docs/examples.py and test_applpy/functional.
- Sum of independent RVs:
x_rv + y_rv or convolution(x_rv, y_rv)
- Sum of IID RVs:
convolution_iid(x_rv, n)
- Product of RVs:
x_rv * y_rv or product(x_rv, y_rv)
- Product of IID RVs:
product_iid(x_rv, n)
- Max/min systems:
Maximum(...), Minimum(...), MaximumIID(x_rv, n), MinimumIID(x_rv, n)
- Order statistic:
OrderStat(x_rv, n, r)
- Mixture model:
mixture([w1, ...], [rv1, ...])
- Transform variable:
transform(x_rv, [[exprs...], [breakpoints...]])
- Truncate support:
truncate(x_rv, [lower, upper])
- Empirical/bootstrapped RV from samples:
bootstrap_rv(sample)
For reliability block diagrams, model series with Minimum* and parallel with Maximum*, then compose subsystems.
Markov-Chain Modeling
Use MarkovChain for discrete-time state-transition requests.
- Build with
MarkovChain(P=..., init=..., states=...) or positional MarkovChain(P, states=...).
- Path and conditional probabilities:
.probability(events, given=...)
- Long-run behavior:
.long_run_probs(method="rational")
- State structure:
.classify_states(), .reachability(), .reducible
- Absorbing-chain questions:
.absorption_prob(state), .absorption_steps()
Use notebook-backed functional tests as behavior references:
test_applpy/functional/test_discrete_time_markov_chain.py.
Output Template
Return runnable code using this shape.
from sympy import Rational
from applpy import ...
from applpy.distributions.continuous import ...
from applpy.distributions.discrete import ...
Then include a short text summary listing key assumptions and computed quantities.
Validation Checklist
Before finalizing, verify:
- Parameters satisfy distribution constraints described in distribution READMEs.
- Mixture weights are nonnegative and sum to
1.
- Support breakpoints and transform/truncation intervals are valid and ordered.
- Requested API names exist in
applpy/__init__.py exports or module paths.
- The returned code includes all imports required to run as-is.
Source Anchors
Use these files as primary references for skill behavior.
docs/examples.pytest_applpy/functional/test_notebook_examples.pytest_applpy/functional/test_paper_examples.pytest_applpy/functional/test_reliability_block_diagrams.pytest_applpy/functional/test_clt_examples.pytest_applpy/functional/test_discrete_time_markov_chain.pyapplpy/distributions/discrete/README.mdapplpy/distributions/continuous/README.md
