On A Closed-Form Estimator of the Shape Parameter of the Three-Parameter Weibull Distribution (Published)
The shape parameter of the three-parameter Weibull distribution () was considered in this study. Known estimation methods like the maximum likelihood, method of moment and maximum product of spacing do not have closed-form estimators for the shape parameter of the three-parameter Weibull distribution rather they involve iterative procedures which may be time-consuming and are less tractable. Dubey (1967), Goda et al (2010) and Teimouri and Gupta (2013) have proposed closed-form estimators for . In this study, a closed-form estimator for is proposed and the proposed estimator is compared with the existing closed-form estimators proposed by the authors mentioned above. To compare the accuracy of the estimators, Monte Carlo simulation is performed. Simulated data from the Weibull distribution are used to check the accuracy of the estimators and the root mean square error (RMSE) is used as a metric for accuracy. The results show that in general, the proposed estimator performs better than the other three closed-form estimators that were compared.
Keywords: Accuracy, Estimators, Parameter, tractability, weibull
Comparative Analysis of Some Selected Classes of Ratio Estimators (Published)
Many ratio type estimators for population mean have come into play in the past. Researchers over the years have been making efforts to improve the efficiency of thee estimators. There has been a lot of modification of some of these estimators. Some forms of comparison have been done in the literature. There is need to further compare these estimators with other existing estimators at varying sample sizes and also considering discrete and continuous distribution. Thirty-eight estimators, five different sample sizes and seven distributions were considered. The population mean estimates and their Bias were computed for the thirty- eight estimators at varying sample sizes under various distribution. The efficiency of the estimator was computed using Mean Square Error (MSE). Using simulation study, it was observed that the efficiency of the estimators increase as sample sizes increases and the estimator performed alike in most distributions
Keywords: Auxiliary variable, Bias, Constants, Estimators, MSE, Mean, Sampling