Approximation of the lognormal distribution as a solution to the sum of lognormal variates

Lognormal distribution is widely used in modeling of variety fields such as fields of sciences and technology, human medicines, linguistics, social sciences and economics and others. In this research projects, three types of approximations, namely Wilkinson approximation, Schwartz and Yeh approximation and Inverse approximation are introduced to determine which approximations worked with the sum of empirical lognormal distributions and approximating its parameter values which will be generated using computational statistics. Throughout the method of computational statistics, the lognormal variates (Xi) will be generated empirically using normal simulation and Monte Carlo simulation by considering variety of simulation conditions such as the number of lognormal variates in the sum, the number of sample size in the variates, independent assumption, identically distributed assumption and non-identically distributed assumption for the lognormal variates. Anderson-Darling goodness of fit test is used to test and determine the best approximation among the three types of approximations. At the end of this research, the best approximation between Wilkinson approximation, Schwartz and Yeh approximation, and Inverse approximation based on the Type I Error rate and the complexness of the approximation's method by considering the number of computational steps and total number of times needed for the analysis is determined.