New Extension of Weibull Distribution: Theory, Properties, and Applications of Water Runoff Data

Abstract

Probability distribution theory offers flexibility in modeling for different categories of data sets. That flexibility of the models makes it suitable for quantifying risks and uncertainties in extreme events. This ia also valuable for decision-making. This study proposed new model as extension of Weibull model, known as exponentiated power alpha index generalized Weibull (EPAIGW).
Graphical study of densities and reliability functions are given for EPAIGW model. Several statistical properties of the new model are derived. For parameters estimation, maximum likelihood method is used. Simulation study is done for EPAIGW model. EPAIGW model is compared with other competitive models to check model performance using water runoff data. This leads to more precise risk assessment, and more solid and economical decisions. It also offers a methodical approach to estimate the probability of unfavourable occurrences and bolstering plans to lesson their effects in fields of epidemiology, climate science, economics and reliability engineering.

Keywords: Weibull; exponentiated; hazard; alpha; simulation; likelihood; runoff; extreme; empirical.

2010 Mathematics Subject Classification. 60E05; 62E15