Calibrated risk-controlling prediction sets for smallholder drought-index insurance triggers under sparse weather-station telemetry: a climate-analytics evaluation of basis-risk-induced payout inequity

Drought-index insurance for smallholders relies on weather-station telemetry that is sparse and unevenly distributed, so the index measured at a station can diverge from the losses experienced on a farm. the present analysis treats that divergence as a distribution-free calibration problem and proposes a conformal risk-controlling framework that converts station-level temperature and rainfall records into prediction sets for farm-level drought status with a user-specified bound on the probability of payout error. The framework is developed formally: a nonconformity score is defined on the joint space of station telemetry and farm-level loss indicators, a split-conformal calibration procedure is stated, and a finite-sample guarantee on the marginal payout-error rate is proved under exchangeability. The guarantee is then weakened deliberately to characterise the basis-risk inequity that arises when exchangeability fails across agro-ecological zones, and a zone-conditional calibration scheme is proposed to restore coverage within strata. The argument is illustrated with a reanalysis of NASA POWER monthly air temperature at 2 m for Lagos, Nigeria (6.52° N, 3.38° E), 2000–2023, 312 monthly observations, mean 26.414 °C, standard deviation 0.943 °C, and a warming trend of 0.1553 °C per decade.