A Study of Linear Model Fitting and Distribution Analysis on Random Numbers Generated in Fortran

Abstract

In this study, we employed Fortran 90 programming to generate pseudorandom numbers ranging from 0 to 1 at various sample sizes (n = 1000, 500, 250, 125, 63, 32, 16, 8). Subsequently, linear fitting models were applied to the generated data. Our findings indicated that the higher sample size of n=1000 yielded the least asymptotic standard error for both slope ‘a’ and intercept ‘b’ parameters in the linear equation. We observed a decrease in the sum of squares of residuals as the sample size (n) decreased, indicating that the linear model also provided a better fit to the data with smaller sample sizes. The consistent nature of the kernel density estimate plots suggests that as the sample size increases, the estimation becomes more precise and less affected by random noise or sampling variability, further enhancing the reliability of the estimated PDF.