Needle roller bearing data analysis method of parameter estimation

In modern statistics, parameter estimation and the parameter estimation of needle roller bearing is a common method of data analysis. In many engineering problems, often meet with a random variable X; Problems of distribution function F ( x( n) ; 0i, 0,', 0x) Known, in the form of parameters, 0n, D,', 0x) To estimate the number of unknown, k; According to the sample value (X x( 1) , x( 2) ,”x( N) To estimate the parameters ( 01, 02,, 0x) To a random variable X; Is this kind of problem in the assessment of parameter estimation. Say simply, parameter estimation is the study of the overall distribution type is known, the unknown parameters, using samples to evaluate these parameters, such as considering the life-span of some electronic elements, overall for X samples; , even if they don't know the distribution of X type, also can use the sample overall X; The average of E ( X) , variance Var ( X) Estimates of electronics life expectancy and life expectancy of volatility. Parameter 0; The point estimator is as follows: 0 = ( x( n) ) 我= 1,- ,m; n = 1, 2, - ,N ( 2 - 23) Type, 0; For the estimator, x ( 1 n) For the case of a sample of the first n data, I I as sample number, m as sample number, n for data serial number, number n for the data. Estimated in a good sense of 0, the point estimation is the search for the estimation of unknown parameters 0 method, requirement of the given method can under certain good conduct at or close to the optimal estimate. Point estimation of parameter are torque estimation and maximum likelihood estimation, the following described respectively. Torque estimation: in 1894 the statisticians Pearson point estimation method of moment estimation is put forward, moment estimation is based on the overall sample moment is moment estimation of consistency, namely the sample moment convergence in probability in the corresponding population moments, in simple terms, as long as the sample size is sufficiently large, sample moment as corresponding overall moment estimates can reach the level of arbitrary precision. According to this principle, moment estimation of k order origin moment of Ak = 1, x ( n) *,i = 1、2。 ,m; n = 1,。 - - - - - - 。 N ( 2 - 24) N type, Ak for the case of a sample I k order origin moment of x ( n) For the first n data, first sample as sample number I, m as sample number, n for data serial number, number n for the data.