{"call_id":"call_ea06e11a","run_id":"20261015T171300Z-suite-closed_form-scripted-9fb914/closed_form.theil.lognormal_s0.5/e1a1","step":"analysis","kind":"tool","name":"core.theil","version":"0.1.0","code_version":"2925aeab2262","inputs":{"dataset":"grid","income":"income","weights":null},"input_digest":"2dbb4603d0dcca4c596d684ad810646150b4a92175ee413c16a5c212ce0cdac1","dataset_digests":{"grid":"e1e1b8d01ef63e459e4b94793b777e7fb1e9f189c51d1343b516f97aef72a6bd"},"result":{"tool":"core.theil","version":"0.1.0","call_id":"call_ea06e11a","status":"ok","reason":"","figures":[{"key":"theil","value":0.12499291905007463,"unit":"index","label":"Theil T index of income (unweighted)","se":null,"ci_low":null,"ci_high":null,"ci_level":null,"derivation":{"steps":[{"text_pt":"Renda média ponderada entre as pessoas com renda positiva.","formula":"μ = Σw·y / Σw","terms":[{"symbol":"Σw·y","value":124264409.37559989,"unit":"","note":""},{"symbol":"Σw","value":100000.0,"unit":"pessoas","note":""}],"result":1242.644093755999,"unit":""},{"text_pt":"Para cada pessoa, r_i = y_i / μ; o índice é a média ponderada de r·ln(r).","formula":"T = Σw·r·ln(r) / Σw","terms":[{"symbol":"Σw·r·ln(r)","value":12499.291905007463,"unit":"","note":"soma ponderada sobre as pessoas"}],"result":0.12499291905007463,"unit":"índice"}],"note_pt":""}}],"diagnostics":[{"name":"n_obs","value":100000,"flag":false,"note":"rows used"},{"name":"weighted_population","value":100000.0,"flag":false,"note":"no weights: the number of rows"},{"name":"weights_used","value":false,"flag":true,"note":"every row counts as one person; wrong for a survey sample"}],"tables":{},"datasets":{},"warnings":["no weight column: every row counts as one person. That is right for a census or an equal-probability sample and wrong for survey data such as PNADc or POF; pass weights="],"assumptions":[],"notes":""},"outputs":null,"output_digest":"2342e8b1b34ad61e4eb5a2aeb243aecfb58aa7262c1033ef639fc1c7818cc834","params_versions":[],"sources":[],"started_at":"2026-10-15T17:13:00.309764Z","duration_ms":73.77866702154279,"error":null,"decided_by":"code","rationale":"","cached":false,"informed_by":[],"model":null,"prompt":null,"response":null,"tokens_in":null,"tokens_out":null,"meta":{}}
