Classes of Ordinary Differential Equations Obtained for the Probability Functions of Gompertz and Gamma Gompertz Distributions
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Abstract
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In this paper, the differential calculus was used to
obtain some classes of ordinary differential equations (ODE)
for the probability density function, quantile function, survival
function, inverse survival function, hazard function and
reversed hazard function of the Gompertz and gamma
Gompertz distributions. The stated necessary conditions
required for the existence of the ODEs are consistent with the
various parameters that defined the distributions. Solutions of
these ODEs by using numerous available methods are a new
ways of understanding the nature of the probability functions
that characterize the distributions. The method can be
extended to other probability distributions and can serve an
alternative to approximation especially the cases of the
quantile and inverse survival functions. Finally, the link
between distributions extended to their differential equations
as seen in the case of the ODE of the hazard function of the
gamma Gompertz and exponential distributions.
Keywords
Q Science (General), QA Mathematics