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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]

Background. A country's agriculture reflects a backbone and performs a vital part in the betterment of the economy and individuals. Facts and figures of the agriculture sector offer a solid foundation and factual pathway intended for upcoming decisions in favor of a country. Accordingly, the probability models have a more significant influence not only in reliability engineering, hydrology, ecology, and medicine but also in agriculture sciences. Objective. The primary objective of this study is to propose a reliable and efficient model for pearl millet yield analysis, thereby empowering decision-makers to make informed decisions about their farming practices. With the successful implementation of this model, farmers can potentially increase their pearl millet yield, leading to higher incomes and improved livelihoods for the rural population of Pakistan. Model. This study proposes a novel probability model, namely, the alpha transformed odd exponential power function (ATOE-PF) distribution, for analyzing pearl millet yield in Punjab, Pakistan. Data. For data collection, two secondary data sets are explored that are electronically available on the site of the Directorate of Agriculture (Economics and Marketing) Punjab, Lahore, Pakistan. Results. The maximum likelihood estimation technique is used for estimating the model parameters. For the selection of a better fit model, we follow some accredited goodness of fit tests. The efficiency and applicability of the ATOE-PF distribution are discussed over the province of Punjab (with RMSE = 4.9176) and Pakistan (with RMSE = 4.5849). Better estimates and closest fit to data among the well-established neighboring models offer robust evidence in support of ATOE-PF distribution as well. [ABSTRACT FROM AUTHOR]