MOMENTS AND MAXIMUM LIKELIHOOD ESTIMATION METHODS FOR WEIBULL DISTRIBUTION

ABSTRACT

This research dives deep into understanding the two-parameter Weibull distribution and how it can be used in practical situations. We used simulation techniques to create datasets with different parameter values and sample sizes. These datasets were then analyzed using methods we discussed earlier, like the method of moments and maximum likelihood estimation. We chose specific parameter values, like λ=1 and k=5, and manually calculated some related values to help us understand how this distribution works. We also looked at quintiles of the Weibull distribution for certain parameter values to see how it behaves. We found that as the quartile percentage increased, the distribution values also increased. We examined statistical measures like average bias and variance for different parameter values and sample sizes. We used the mean square error to check how accurate our parameter estimation methods were. What we discovered was that as we had more data (larger sample sizes), our estimations became more accurate. Furthermore, we explored the theoretical aspects of the Weibull distribution, revealing that it's skewed and follows a particular type of curve called "leptokurtic" for various parameter values. In summary, this study shows that the two-parameter Weibull distribution is quite useful for modeling real-world data. We've gained valuable insights into how it behaves, how to estimate its parameters, and how it performs statistically. This knowledge can be applied across various fields and situations.