Insurance serves as a mechanism to effectively manage and transfer revenue-related risks. We conducted a study to explore the potential financial advantages of index insurance, which protects agricultural producers, specifically sugarcane, against excessive rainfall. Creation of the index involved utilizing generalized additive regression models, allowing for consideration of non-linear effects and handling complex data by adjusting the complexity of the model through the addition or reduction of terms. Moreover, quantile generalized additive regression was deliberated to evaluate relationships with lower quantiles, such as low-yield events. To quantify the financial benefits for farmers, should they opt for excessive rainfall index insurance, we employed efficiency analysis based on metrics such as conditional tail expectation (CTE), certainty equivalence of revenue (CER), and mean root square loss (MRSL). The results of the regression model demonstrate its accuracy in predicting sugar cane yields, with a split testing R² of 0.691. MRSL should be taken into consideration initially, as it is a farmer’s revenue assessment that distinguishes between those with and those without insurance. As a result, the GAM model indicates the least fluctuation in farmer income at the 90th percentile. Additionally, our study suggests that this type of insurance could apply to sugarcane farmers and other crop producers in regions where extreme rainfall threatens the financial sustainability of agricultural production.

In this paper, we introduce a new continuous distribution mixing exponential and gamma distributions, called new Sushila distribution. We derive some properties of the distribution include: probability density function, cumulative distribution function, expected value, moments about the origin, coefficient of variation (C.V.), coefficient of skewness, coefficient of kurtosis, moment generating function, and reliability measures. The distribution includes, a special cases, the Sushila distribution as a particular case p=1/2 (θ = 1). The hazard rate function exhibits increasing. The parameter estimations as the moment estimation (ME), the maximum likelihood estimation (MLE), nonlinear least squares methods, and genetic algorithm (GA) are proposed. The application is presented to show that model to fit for waiting time and survival time data. Numerical results compare ME, MLE, weighted least squares (WLS), unweighted least squares (UWLS), and GA. The results conclude that GA method is better performance than the others for iterative methods. Although, ME is not the best estimate, ME is a fast estimate, because it is not an iterative method. Moreover, The proposed distribution has been compared with Lindley and Sushila distributions to a waiting time data set. The result shows that the proposed distribution is performing better than Lindley and Sushila distribution.

Insurance serves as a mechanism to effectively manage and transfer revenue-related risks. We conducted a study to explore the potential financial advantages of index insurance, which protects agricultural producers, specifically sugarcane, against excessive rainfall. Creation of the index involved utilizing generalized additive regression models, allowing for consideration of non-linear effects and quantile generalized additive regression to evaluate relationships with lower quantiles, such as low yield events. To quantify the financial benefits for farmers, should they opt for excessive rainfall index insurance, we employed efficiency analysis based on metrics such as Conditional Tail Expectation, Certainty Equivalence of Revenue, and Mean Root Square Loss. The results of the regression model demonstrate its accuracy in predicting sugar cane yields, with a split testing R2 of 0.691. Additionally, our study suggests that this type of insurance could also apply to sugarcane farmers and other crop producers in regions where extreme rainfall threatens the financial sustainability of agricultural production.