Development of a Novel Discrete Distribution Family from a Continuous Model: Applications to Health, Agricultural and Crop-Based Fertilizer Data

Abstract

In recent years, global environmental and economic issues have become more severe, making sustainable production a key priority around the world. This study presents a new discrete family of statistical distributions derived from the Odd Nadarajah-Haghighi-G (ONH-G) family. This method uses a partitioning technique that transforms the continuous ONH-G family into a discrete counterpart called the two-parameter Discrete Odd Nadarajah-Haghighi-G (DONH-G) family. Several statistical properties of this new family are derived, including the probability mass function, cumulative distribution function, quantile function, moments, and various types of entropy. Parameter estimation for the discrete family is performed using the maximum likelihood method. To illustrate the ability of this family to generate discrete distributions from continuous distributions, the exponential distribution is used as an example. Production data from a local factory are analyzed to evaluate sustainability and demonstrate the resilience of the proposed distribution. Maximum likelihood estimation is applied to estimate the parameters, and the theoretical behavior of the model is validated through simulations on sample data sets. The results are promising and provide a useful framework for researchers interested in transforming continuous distributions into discrete forms, facilitating the modeling of discrete data, such as production sustainability, environmental data, and other related phenomena.