期刊名称：Lecture Notes in Engineering and Computer Science
印刷版ISSN：2078-0958
电子版ISSN：2078-0966
出版年度：2018
卷号：2233&2234
页码：225-230
出版社：Newswood and International Association of Engineers
摘要：Lévy distribution is one of few stable
distributions. The absence of closed form of some of the
probability functions of distribution has inspired researchers
into finding alternate options such as approximations. In this
paper, homogenous ordinary differential equations (ODES) of
different orders were obtained for the probability density
function, survival function, hazard function and reversed
hazard function of Lévy distribution. This is possible since the
aforementioned probability functions are differentiable.
However, approximation remains the only option for the
quantile function and inverse survival function of the
distribution. This is because those functions may not be
reduced to an ODE as a result of the intractable nature of the
cumulative distribution function which is used in obtaining
them. . Differentiation and modified product rule were used to
obtain the required ordinary differential equations, whose
solutions are the respective probability functions. The different
conditions necessary for the existence of the ODEs were
obtained and it is in consistent with the support that defined
the various probability functions considered. The parameters
that defined each distribution greatly affect the nature of the
ODEs obtained. This method provides new ways of classifying
and approximating other probability distributions apart from
one considered in this research. Algorithms for implementation
can be helpful in improving the results.
