Maximum Likelihood Estimation And Application Of Marshall-olkin Fréchet Disdribution Parameters

In order to increase the flexibility of index distribution family in application,we usually extended the distribution family,which is involved in many literatures.Marshall and Olkin proposed a new method for extending distribution family,adding a parameter to the distribution group.According to this method,we get the Marshall-Olkin extension form of Fréchet distributed,named Marshall-Olkin Fréchet distribution.This paper studies the maximum likelihood estimation and application of Marshall-Olkin Frechet distribution.First,the paper focuses on the maximum likelihood estimation of the distribution parameters of the extended distribution group Marshall-Olkin Fréchet,including some known as unknown parameters of maximum likelihood estimation,the truncated samples under the maximum likelihood estimation of unknown parameters,as well as in sequence under the constraints of multiple Marshall-Olkin Fréchet distribution of population parameter of maximum likelihood estimation.At the same time,using the MATLAB language,the real data of the continuous failure interval of the jet air conditioner system is brought in,and the maximum likelihood estimate of the parameters is obtained.On this basis,deducing the failure rate of air conditioner.Secondly,the paper focuses on the application of the Marshall-Olkin Fréchet distribution,and applies the Marshall-Olkin Fréchet distribution to the product quality testing.Firstly,the minimum sample size needs to be considered in terms of both large and small batches based on the acceptance of the quality of the consumers.On this basis,considering the ratio between the true value of the product life time and the average life time of the minimum product,the probability of the producer receiving the product is obtained.Finally,the minimum life time for products that meet consumer and producer needs.Finally,we applied the Marshall-Olkin Fréchet distribution to the time series model,considering the Marshall-Olkin Fréchet distribution as the marginal distribution of first-order autoregressive model in the following three and MAX AR ? ?(1)model,the MAX-MIN AR(1)the model structure,Marshall-Olkin Fréchet distribution related properties,and proof is given.