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This research introduces a novel probability model, the DUS modified Lehmann-type II power function distribution, designed to optimize potato yields. This model provides valuable insights for decision-makers and can enhance sustainable potato production practices. To achieve our goal, we utilized a time series dataset spanning 75 years (1947–1948 to 2021–2022) of potato cultivation statistics for Punjab and Pakistan, sourced from the official website of the Agricultural Statistics of Pakistan. We rigorously tested six parameter estimation methods, ultimately selecting the maximum likelihood technique based on extensive simulation experiments that considered accuracy measures, including bias, mean square, and root mean square errors. Model selection was determined using established goodness-of-fit tests among recognized models. The precise estimations generated by our model offer valuable support to producers and policymakers in making well-informed decisions about crop management strategies, including the optimal use of fertilizers and pesticides. [ABSTRACT FROM AUTHOR]