ESTIMATION OF UNKNOWN PARAMETER OF WEIBULL DISTRIBUTION IN INCOMPLETE MODELS OF STATISTICS
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Abstract:
This paper will discuss the estimation results of Weibull distribution with type 1 right-censored data using numerical methods. These methods involve simulations employing the Maximum Likelihood Estimation technique, utilizing both the Quasi-Newton rule and the Nelder-Mead simplex algorithm. The simulation includes generating random sample data from distribution with sample n sizes of 500 and 1000. The parameters used for the initial guess are obtained from example data of patients with lung cancer, specifically . Based on the simulation results of the two estimation methods, it is evident that parameter estimation using the Quasi-Newton rule outperforms the Nelder-Mead simplex algorithm when in an uncensored state. However, the estimated results of the Nelder-Mead method show better estimated values compared to the Quasi-Newton rule after a fixed censoring time. [see, graphs and tables below].
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