Minimum-Distance Estimation oftheParameters of the3-Parameter Weibull Distribution

Purposeo: Widenstate-of-the-art Special mathneeded forexplanation: Probability andstatistics Special mathneeded touseresults: Statistics A methodforobtaining themaximum likelihood Results useful to: Reliability theoreticians. estimators forthe3-parameter Weibull distribution (1)was used.ThemethodofLemon(3)couldalsobeused. Abstract-A 3-phase estimation technique isdeveloped andappliedLemon's method reducesntheproblem ofsol tee tothe3-parameter Weibull distribution using location improvement through minimum-distance estimation techniques. A MonteCarloiterative equations tothatofsolving justtwoiterative analysis wasconducted onfive members ontheWeibull distribution equations andonedeterministic equation. (shape parameter 0.5, 1(1)4) with sample sizes of4(4)20. Eachsample size The goodnessoffitstatistics usedintheminimum wasdrawn1000times fromeachofthedistributions. Threenew distanceestimationof the locationparameterare estimators weredeveloped. Allthenewestimators werecompared with Kolmogorov (K-S) distance, Cramer-von Mises(CVM) maximumlikelihood estimators. Thecriteria forcomparison wasthe ratio ofthemeansquare errors oftheparameter estimates. Allofthenew distance andAnderson-Darling (A-D)distance (2). A estimators provided better estimates thanthemaximumlikelihood technique similar totheoneusedinthis paperwasapplied estimators. Thetechnique using theAnderson Darling statistic providedto the3-parameter Gamma distribution (2).However, thebest overall estimates oftheparameters. without anextensive MonteCarlo verification, onedoesn't knowapriori that asimilar improvement overmaximum likelihood estimation obtained forthe3-parameter Gam- ma wouldbeachieved forthe3-parameter Weibull