Classes of Ordinary Differential Equations Obtained for the Probability Functions of Half-Cauchy and Power Cauchy Distributions

摘要

In this paper, the differential calculus (productudrule) was used to obtain some classes of ordinary differentialudequations (ODE) for the probability density function, quantileudfunction, survival function, inverse survival function, hazardudfunction and reversed hazard function of the half-Cauchy andudpower Cauchy distributions. The stated necessary conditionsudrequired for the existence of the ODEs are consistent with theudvarious parameters that defined the distributions. Solutions ofudthese ODEs by using numerous available methods are newudways of understanding the nature of the probability functionsudthat characterize the distributions. The method can beudextended to other probability distributions and can serve anudalternative to approximation especially the cases of theudquantile and inverse survival functions