Parameter estimation method based on beta likelihood function

Abstract

Disclosed is a parameter estimation method based on a beta likelihood function. The parameter estimation method based on the beta likelihood function includes four steps: step 1, collecting failure data; step 2, calculating an average rank; step 3, selecting life distribution and constructing the beta likelihood functions; step 4, working out a life distribution parameter. The parameter estimation method based on the beta likelihood function calculates beta distribution of product reliability obedience when each test piece breaks down according to a beta distribution method in nonparametric estimations of reliability degrees, and then uses the probability density of the beta distribution to measure rational degrees of reliability degree estimation values of all the test pieces when the test pieces break down, uses an arithmetic product of the rational degrees of the reliability degree estimation values of all the test pieces when the test pieces break down to construct the beta likelihood function, and uses a distribution parameter which enables value of the beta likelihood function to be maximum as an estimation result. The parameter estimation method based on the beta likelihood function has extensive applicability in the reliability data analysis field.

Description

technical field [0001] The invention relates to a parameter estimation method based on a β likelihood function, which is a parameter estimation method involving a probability distribution, belongs to the field of mathematical statistics, and is suitable for but not limited to the field of reliability data analysis. Background technique [0002] The parameter estimation of the probability distribution is a method of estimating the unknown parameters contained in the population distribution based on the samples drawn from the population. Common parameter estimation methods include moment estimation, least square estimation, and maximum likelihood estimation. These methods have their own advantages, but they also have disadvantages: the availability of moment estimation and least squares estimation depends on the mathematical form of the selected distribution, such as the distribution that cannot be transformed into a linear structure by taking logarithms and other operations. ...

AI Technical Summary

Problems solved by technology

These methods have their own advantages, but they also have disadvantages: the availability of moment estimation and least squares estimation depends on the mathematical form of the selected distribution, such as the distribution that cannot be transformed into a linear structure by taking logarithms and other operations. The least squares estimation; while the maximum likelihood estimation examines the probability density of each specimen occurrence, when the probability density of the selected distribution at a certain specimen occurrence can be infinite, the maximum likelihood estimation is invalid

However, the maximum likelihood estimation "maximizes the product of the probability density estimates of each individual failure (death) of the current sample" and "makes the most reasonable reliability (survival rate) estimation value of each individual failure (death) of the current sample" are not equivalent, i.e. theoretically problematic to use maximum likelihood estimation in reliability or survival studies

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