Estimation of the Shape Parameter for Lomax Distribution Under Bilateral Type-I Censored Sample

Abstract

The maximum likelihood estimation of shape parameters of Lomax distribution under bilateral Type-I Censored Sample is studied, the explicit expression of shape parameter estimation cannot be obtained, but it is proved that the maximum likelihood estimation of this parameter is unique. Then the EM estimation of shape parameters is obtained by using EM algorithm, and the asymptotic variance and approximate confidence interval of the EM estimation of shape parameters are also given; Finally, the effects of maximum likelihood estimation and EM estimation of shape parameters of Lomax distribution are numerically simulated. By comparing the relative deviation, it shows that the estimation effect of using EM algorithm to calculate shape parameters is relatively good, and the asymptotic variance and asymptotic confidence interval of EM estimation are given.

The Interval Estimation and Hypothesis Test of the Parameter from Inverse Topp-Leone Distribution under Type-II Censored Sample

“…For the life research of products, the commonly used test is the censoring test, of which type-Ⅱcensoring and type-I censoring are two common censoring tests. Statistical inference for these two types of censored samples has produced rich research results [3][4][5][6][7][8][9] . Up to now, no literature has studied the parameter estimation and hypothesis test of the inverse Topp-Leone distribution under type-Ⅱcensored samples.…”