A Kind Of Generalized Weibull Distribution Of Statistical Inference

In this paper，we obtain a new two-parameter life distribution as well as therelated analysis for this new distribution. For this new distribution, we have thefollowing results:(1) The monotonicity of the probability density function and thefailure rate function are discussed, besides the theoretical proof of the orderstatistics is also given (2) For the full sample, the moment estimation, the maximumlikelihood estimation (MLE) and the inverse moment estimation are given. When theparameter is known, the existence and uniqueness of MLE and the inversemoment estimation are proved. While the parameter is known, we only prove theexistence of MLE and discuss the existence and uniqueness of the inverse momentestimation. With respect to the mean square error (MSE), the moment estimation,MLE and the inverse moment estimation are compared by using the Monte-Carlosimulation. When the parameter is known, MLE is the best, next is the momentestimation, the second method of the inverse moment estimation is the worst of all.While is known, MLE is the best, next is the second method of the inversemoment estimation, the first method of the inverse moment estimation is the worstof all.(3) For the type-Ⅱcensored sample, when the parameter is known, theexistence and uniqueness of the inverse moment estimation is proved. While theparameter is known, we only prove the existence of MLE and the inverse momentestimation. When one parameter is known and the other is unknown, the MSE, theMLE and the inverse moment estimation are discussed and compared by theMonte-Carlo simulation, the best is MLE, next is the modified inverse momentestimation, the unmodified inverse moment estimation is the worst (4) At the end ofthis paper, when one parameter is known and the other is unknown, the relatedinterval estimation is given by two methods. When the parameter is known，theinterval estimation of is compared by the Monte-Carlo simulation, the firstmethod is better. When the parameter is known, the interval likelihoodestimation of is given by using the Monte-Carlo simulation.