PSO-KS Algorithm for Fitting Lognormal Distribution: Simulation and Empirical Implementation to Women’s Age at First Marriage Data

Abstract

Lognormal distribution plays an essential role in the distribution modeling of right-skewed data in many areas. In social sciences, for instance, it can be used to model women’s age at first marriage pattern, a key indicator in studying fertility patterns. Distribution fitting is a fundamental and essential stage of data modeling before doing advancing the analysis. Kolmogorov-Smirnov (KS) distance is applicable as maximum goodness-of-fit (GOF) estimators for distribution parameters. Minimizing KS distance is optimization problem. Particle swarm optimization (PSO) algorithm is a general optimizer that can handle various optimization problems. This study assesses the characteristics of minimum KS distance estimator for lognormal distribution parameters. KS distance estimators were obtained via optimization using the PSO algorithm, so the combination of these is called the PSO-KS algorithm. We conducted a simulation to assess the performance of PSO-KS, Maximum Likelihood (MLE), Method of Moment (MME). The bias and mean square error (MSE) of point estimators were used in simulation to assess the characteristics of estimators. Meanwhile, MSE of distribution fitting, KS distance, and log-likelihood value were used to evaluate the GOF characteristics. Moreover, we demonstrated the performance of the algorithm by implementing it to women’s age at first marriage data in Indonesia. The results show that based on the bias and MSE properties, the PSO-KS point estimators yield similar characteristics with MLE, but better than MME. From the GOF perspective, PSO-KS outperforms in MSE of distribution fitting and KS distance, but not in log-likelihood value. We also observed these patterns in the women’s age at first marriage data. The contributions of this study are two-fold, first to assess the PSO-KS algorithm in the lognormal distribution case. Second, it implements the algorithm on women’s age at first marriage data, which has broad social, economic, and public health implications.