Ordinary Differential Equations of the Probability Functions of the Weibull Distribution and their Application in Ecology
Weibull distribution has been applied to many areas in ecological studies and engineering. Application of the Weibull and other probability distributions in ecology are mainly in fitting ecological data which is very vital in revealing latent characteristics of the object of study. The use of the ordinary differential equations (ODE) in fitting has not been studied in ecological studies. Ordinary differential calculus was used to obtain the homogenous ODE of the probability density function (PDF), quantile function (QF), survival function (SF), inverse survival function (ISF), hazard function (HF) and reversed hazard function (RHF) whose solutions are their respective functions of the Weibull distribution. Different classes of ODEs were obtained. The novelty of this proposed method is applied to radiation data.
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