Modeling Climate data using the Quartic Transmuted Weibull Distribution and Different Estimation Methods

Abstract

Researchers from various fields of science encounter phenomena of interest, and they seek to model the occurrences scientifically. An important approach of performing modeling is to use probability distributions. Probability distributions are probabilistic models that have many applications in different research areas, including, but not limited to, environmental and financial studies. In this paper, we study a quartic transmuted Weibull distribution from a general quartic transmutation family of distributions as a generalization and an alternative to the well-known Weibull distribution. We also investigate the practical application of this generalization by modeling climate-related data sets and check the goodness-of-fit of the proposed model. The statistical properties of the proposed model, which includes non-central moments, generating functions, survival function, and hazard function, are derived. Different estimation methods to estimate the parameters of the proposed quartic transmuted distribution: the maximum likelihood estimation method, the maximum product of spacings method, two least-squares-based methods, and three goodness-of-fit-based estimation methods. Numerical illustration and an extensive comparative Monte Carlo simulation study are conducted to investigate the performance of the estimators of the considered inferential methods. Regarding estimation methods, simulation outcomes indicated that the maximum likelihood estimation (MLE), Anderson-Darling estimation (ADE) and right Anderson-Darling (RADE) methods in general outperformed the other considered methods in terms of estimation efficiency for large sample size, while all considered estimation methods performed almost same in terms of goodness-of-fit regardless the values of shape and transmuted parameters. Two real-life data sets are used to demonstrate the suggested estimation methods, the applicability and flexibility of the proposed distribution compared to Weibull, transmuted Weibull, and cubic transmuted Weibull distributions. Weighted least squares estimation (WLSE) and least squares estimation (LSE) methods provided best model fitting estimates of the proposed distribution for Wheaton River and rainfall data respectively. The proposed quartic transmuted Weibull distribution provide significantly improved fit for the two datasets as compared with other distributions.