Classes of Ordinary Differential Equations of Length Biased Exponential Distribution and their Solutions

Abstract

The purpose of the work is to generate the ordinary differential equations and their solutions for the probability density function, quantile rate function, survival rate function, inverse survival rate function, haz-ard rate function and reversed hazard rate function of the Length Biased Exponential Distribution. The ordinary differential equations and their so-lutions are obtained using the Math of differentiation and integration as a tool together with their boundary conditions. The boundaries and para-meters that portrayed the distribution unavoidably decide the nature, presence, uniqueness, arrangement and the various possible solutions of these ordinary differential equations are better approaches to understand these characteristics. The work will be helpful to analyze the lifetime growth or risk and is of great significance in the field of ecological studies. The method can be very useful for the other probability distributions and can serve as a substitute for the approximation study.