On the Study of Kumaraswamy Reduced Kies Distribution: Properties and Applications

Abstract

Unit-bounded distributions play a crucial role in probability and statistics for modeling quantities that are strictly confined between 0 and 1, such as rates, ratios, proportions, and percentages. Despite their importance, these distributions are relatively scarce compared to those with unbounded support, even though many real-world phenomena involve data restricted to a unit interval, including proportions, percentages, ratios, rates, and fractions. Some unit distributions arise naturally from analytical derivations, while others emerge through generalization from distributions originally defined over broader domains. This study introduces a three-parameter unit-bounded distribution, termed the Kumaraswamy Reduced Kies Distribution, developed through a generalization process of Kumaraswamy G-family of distribution based on the function of functions approach applied to the Reduced Kies Distribution proposed. The Kumaraswamy Reduced Kies Distribution, a flexible three-parameter distribution with semi-bounded support, serves as the foundation for extending this adaptability to the unit interval. The probability density function of the proposed distribution exhibits a variety of shapes, including J, reversed-J, left-skewed, symmetric, and bathtub unimodal forms. Additionally, its hazard rate function follows a monotonically non-decreasing pattern. Several statistical properties and reliability measures are examined, including the survival function, hazard rate function, cumulative hazard function, reversed hazard function, odd function, quantile function, median, skewness, kurtosis, and order statistics. The estimation of model parameters is performed using Maximum Likelihood Estimation, Maximum Product of Spacing, and Cramer-von Mises methods. Monte Carlo simulations are conducted to assess the effectiveness of these estimation techniques, demonstrating that Biases, Mean Squared Errors, and Mean Relative Errors decrease as the sample size increases. Finally, the practical applicability of the proposed model is illustrated using two real-life datasets. A comparative analysis confirms that the proposed model achieves a superior fit compared to several existing models.