A Simulation Based Comparative Study to Find Efficient Parameter Estimation Methods for Weibull Distribution
Keywords:Weibull distribution, the maximum likelihood method, the least square method, the weighted least square method, median rank regression method, Kolmogorov-Smirnov test.
This paper aims to find efficient methods for estimating the parameters (shape =α , scale = β ) of Weibull distribution in different situations. The maximum likelihood estimation method (MLE), the median rank regression method (MRR), the least square method (LSM) and the weighted least square method (WLSM) are considered for the estimation of the parameters. The root mean square error (RMSE) criterion is used to measure the relative efficiency of the estimators experimentally (Monte Carlo simulation). From the simulation study, it is observed that the MLE produces the lowest RMSE, irrespective of all sample sizes, for decreasing hazard function(α << β ) (α is considerably smaller than β ) and roughly linear hazard function with a positive slope (α >1) . When (α >> β ) the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) but for large sample sizes it is the MLE, irrespective of all types of hazard functions. When (α ,β →1), the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) and the MLE for large sample sizes irrespective of all types of hazard functions. This pattern becomes reversed whenα and β have the larger value. Only the MLE gets stuck when the hazard function is parallel to Y − axis (α >> β ) and the WLSM is suitable in such a situation (lowest RMSE) irrespective of all sample sizes. Finally, the utility of simulation results have been illustrated by analyzing two real-life data sets.
Dhaka Univ. J. Sci. 71(1): 17-25, 2023 (Jan)