The Parameter Estimation And Comparison Of Means Of Lomax Distribution

This paper discusses the problem of Bayesian estimation of parameter and comparison of means from the two-parameters Lomax distribution.Firstly, under the assumption that the scale parameter λ is known, we study the problem of Bayes estimation of the parameter θ based on record values from the two-parameters Lo-max distribution. On the basis of it, we may use the moment estimation approach to get the estimation of prior parameters a and b and get the empirical Bayes estimation of parameter θ. Then we give the discussion of admissibility of estimators in the form of (cT+d)-1based on Gamma prior density. In order to compare the mean squared errors of different estimators, Monte-Carlo simulations are used. It showed that empirical Bayes estimation are better than the Bayes estimation with respect to different loss functions.Secondly, under the assumption that both the parameter λ and θ are unknown, we use the Soland method to estimate the two parameters at the same time. Then we get the predictive interval of future record. Finally, in order to assess the performances of the the Soland method, a Monte-Carlo simulations study is used.Lastly, we discuss the problem of the comparison of means from the Lomax distribution of the same scale parameter, first of all, the comparison of means will be transformed to the comparison of the shape parameter using the characteristic of the Lomax distribution. Finally, we obtain the generalized p-value.