Classes of Ordinary Differential Equations Obtained for the Probability Functions of Gumbel Distribution


In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODEs) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the Gumbel distribution. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions, functions and can serve an alternative to approximation and estimation

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