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  "Date": "2026-10-05",
  "Title": "Evaluation of Tweedie Exponential Family Models",
  "Authors@R": "person(\"Peter K.\", \"Dunn\", email = \"pdunn2@usc.edu.au\", role = c(\"cre\", \"aut\") )",
  "Encoding": "UTF-8",
  "Description": "Maximum likelihood computations for Tweedie families,\nincluding the series expansion (Dunn and Smyth, 2005;\n<doi:10.1007/s11222-005-4070-y>) and the Fourier inversion\n(Dunn and Smyth, 2008; <doi:10.1007/s11222-007-9039-6>), and\nrelated methods.",
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  "Date/Publication": "2026-10-21 07:23:30 UTC",
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  "Author": "Peter K. Dunn [cre, aut]",
  "Maintainer": "Peter K. Dunn <pdunn2@usc.edu.au>",
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    "id": "00917db1e35bbd86355e24b9c28d51290c1751d8",
    "author": "Claude <noreply@anthropic.com>",
    "committer": "Peter Dunn <pdunn2@usc.edu.au>",
    "message": "Inversion: adaptive quadrature for p < 4/3; tail convergence test\n\nTwo faults in TweedieIntegration, both seen in\nptweedie_inversion(0.001, mu = 5, phi = 10, power = 1.01).\n\n1. Missed oscillations, p < 4/3 (wrong answers, no warning).\n   The regions run between the zeros of the integrand, found from the\n   levels Im k(t) = m pi, assuming Im k(t) crosses each level once on each\n   side of its maximum. With A = (2-p)/(p-1) > 2 (p < 4/3), (1 + i x)^alpha\n   winds round the origin while it decays, so Im k(t) oscillates about\n   zero before the -t y term takes over, and one region (e.g. [7.9, 15708]\n   after scaling) held all of those oscillations in [7.9, 200], where the\n   512-point rule has 36 nodes. F was wrong by 2e-5 here, and by up to\n   2e-3 elsewhere (y far below mu, p <= 1.2), without a warning.\n   Now: for p < 4/3, every region is integrated by GaussAdaptive (new),\n   which halves the interval with the largest error estimate until the\n   total is below max(aimrerr, 1e-13) times the scale (the integral of\n   |integrand|, and pi/2 for the CDF). For p >= 4/3 Im k(t) has a single\n   maximum (proof in the comments), so one rule is used, as before.\n\n2. Tail convergence test (spurious warnings, platform dependent).\n   The acceleration stopped when the change in the tail estimate W was\n   below 1e-12 relative to |W| + 1e-12. When the tail is negligible, its\n   areas are rounding noise: exactly 0 on some platforms (0/1e-12 = 0:\n   converges), ~1e-17 on others (1e-17/1e-12: never converges, runs to\n   400 regions and warns). Now the change may instead be small relative\n   to the whole integral (or pi/2 for the CDF).\n\nChecked on 6600 cases (y, mu, phi, p grid; F, 1 - F, density) against the\nseries (1 < p < 2) and the inverse Gaussian (p = 3): 63 values more\naccurate, none less; 58 needless warnings removed; 27 new density\nwarnings, all on values the inversion really gets wrong. Run time\nunchanged for p >= 4/3 (faster for 1.5 <= p < 2: fewer regions), about\n3x for p <= 1.",
    "time": 1792567410
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      "title": "Evaluation of Tweedie Exponential Family Models",
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