Least squares estimation of Weibull distribution with type I interval deletion
A parameter estimation method based on the properties of cumulative distribution function and exponential distribution order statistic,called NLSE method,is proposed to address the problem that the type Ⅰ interval missing data have not closed form solutions.This method converts the probability distribution function into a cumulative density function,establishes a two parameter Weibull distribution model,constructs a regression form using Weibull linear transformation,and uses the least squares estimation method for parameter estimation.Furthermore,to enhance the method,interval-sampled observational data is incorporated into the NLSE framework,resulting in an improved method termed the PNLSE method.Monte Carlo numerical simulation was conducted to compare and evaluate the NLSE method,PNLSE method and MLE method using two indicators of deviation and mean square error.The results showed that the proposed method was competitive with the MLE method.In addition,a set of engine starter replacement data from a training unit of PA44 aircraft was used for empirical analysis to further verify the superiority of the PNLSE method.
type Ⅰ interval deletionWeibull distributionlinear regression modelMonte Carlo simulationleast squares estimation
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