A robust evaluation of the exponential-logarithmic distribution and its application to trade credit period data for perishable goods (a case study of Agbor Fruit Market, Agbor, Delta State)

Abstract

In this work, the Exponential-Logarithmic Distribution (ELD) was used to analyze real-life data, and some properties of the distribution were discussed with the help of the Mathematica software. Simulation study was also carried out for different values of the parameters of some distributions with the aid of the mathematical package, and observations were recorded. Comparison between the theoretical moments and the raw moment shows that the Exponential-Logarithmic distribution is a good fit for the data. The method of maximum likelihood estimation was used (mle) to estimate the model parameters. The score function could not be solved directly since it is a non-linear system of equation and the Newton Raphson’s iterative method was used for the numerical computation of the parameter estimates. This was achieved with the use of the mass, stat4, nacopula and fitdistrplus packages in R software. The model was applied to a real-life problem on the length of time (trade credit period) it takes a retailer to pay back goods bought on credit from the supplier before he is debt free in Ika-south local government area, Delta state and prediction was made with the aid of the survival and the hazard function. At time zero, the probability of “survival” (that is the probability that a retailer remains a debtor immediately after the purchase is 1.0). This is the same as saying that 100% of retailers remain debtors immediately after purchase. Now, the median survival is approximately 26 hours. Thus, the length of time (credit period) from after purchase that half of the retailers receive trade credit funding is 26 hours that is to say, half of them will “survive” trade credit funding after 26 hours.