moveq-core

Pure NumPy algorithms for measuring transport equity.

This is the calculation engine of the moveq stack. It has no I/O: you pass NumPy arrays (or, with the optional frames extra, a pandas DataFrame) and get numbers and small result objects back. There is no database, GIS library, or network client.

Most applications should install the umbrella package moveq, which re-exports this API. Install moveq-core directly only when you want the metrics without the catalogue registry.

What each metric is for

Transport analysis usually has a service variable per area (trips, departures, coverage) and a population weight. Sometimes there is also a socioeconomic rank (deprivation index, income band).

Population-weighted Gini

Gini answers: how unevenly is this service spread across people?

Areas are sorted from lowest to highest service. Cumulative population share is plotted against cumulative service share (a Lorenz curve). Gini is 1 minus twice the area under that curve, using trapezoidal integration.

• 0 — every person faces the same service level (including the all-zero convention: nothing to distribute)
• toward 1 — almost all service sits with a small share of the population

Gini does not know whether the poorly served people are deprived. It is a statement about the service distribution only.

Palma ratio

Palma answers: how does the best-served tenth compare with the worst-served two-fifths?

It is the population-weighted mean service of the top 10% divided by that of the bottom 40% (areas on the boundary of those shares are split proportionally). Equal service, including all-zero service, gives 1. If the bottom 40% have zero service while the top 10% do not, the function returns inf rather than dividing by zero.

Palma is more sensitive to the tails than Gini, which is why the two are reported together.

Wagstaff Concentration Index

The concentration index answers: does service rise or fall as deprivation falls?

Areas are ordered by rank (1 = most deprived by convention in this library). Units that tie on rank share the group's midpoint fractional rank, so the answer does not depend on input order. Unpopulated units are ignored. A population-weighted covariance between service and fractional rank is scaled by the mean service. For non-negative service the result is in [-1, 1]:

This is the metric to use when the policy question is about socioeconomic targeting, not only about overall unevenness.

Composite score with missing-term renormalisation

compute_score builds a 0–100 weighted index from named terms in [0, 1]. The important behaviour is what happens when a term is None:

1. that term is dropped, not treated as zero
2. remaining design weights are renormalised to sum to 1
3. the result records weight_used vs design_weight, the dropped ids, and a note

If every term is missing, score is None. Design weights must be finite and strictly positive; non-finite term values are rejected rather than clipped. Callers keep control of which indicators exist; the library refuses to invent a zero.

Optional DataFrame helpers (moveq_core.frames)

With pip install "moveq-core[frames]" (or "moveq[frames]"):

• vulnerability index — min-max scale several deprivation-like columns to 0–100 and take the row-wise mean
• multiply deprived — flag areas that sit in the worst tertile on at least k factors at once

These are convenience summaries, not a substitute for a national IMD.

Formulae: methodology.

Installation

Requires Python 3.10+. Runtime dependency: numpy>=1.24.

pip install moveq-core
pip install "moveq-core[frames]"   # pandas helpers

Quickstart

import numpy as np
from moveq_core import (
    compute_gini,
    compute_palma_ratio,
    compute_concentration_index,
    gini_result,
    compute_score,
)

service = np.array([10.0, 20.0, 5.0, 50.0, 8.0])
population = np.array([1000, 800, 1200, 300, 900])
deprivation_rank = np.array([1, 3, 2, 5, 4])  # 1 = most deprived

gini = compute_gini(service, population)
palma = compute_palma_ratio(service, population)
ci = compute_concentration_index(
    service, deprivation_rank, population, rank_direction="higher_is_advantaged"
)
gini_audit = gini_result(service, population)  # EquityResult: value, method, n_areas, …

score_res = compute_score(
    terms={"coverage": 0.75, "evening": 0.50, "night": None},
    weights={"coverage": 0.50, "evening": 0.30, "night": 0.20},
)
print(score_res.score, score_res.dropped, score_res.note)

Documentation

• Methodology
• API reference
• Umbrella package
• Source
• Changelog

License

BSD 3-Clause.