Approximate Confidence Region Of Parameters For Several Distributions Under Type-I Life Test

In this paper, we study the type-I life test of lognormal, normal and Weibull distributions with large numbers of samples, get the approximate confidence regions of the parameters, and do many stochastic simulations on the theoretical basis with computer.In the case of lognormal distribution, we obtain the limit distribution of the sum of the logarithm of every sample's test time, and construct the pivot. By the two-step-method, which is given in this paper, we can obtain the associated approximate confidence region of parameters.As to normal distribution, we find the pivot, which we get from the limit distribution of total test time, is approximate with the one from the case of lognormal distribution. So we can get the confidence region in the same way.About Weibull distribution, we also obtain the limit distribution of total test time and construct the pivot. After coordinate transformation, we can get the approximateconfidence region of parameters in virtue of the approximate expression of e.Large numbers of stochastic simulations show that the results are comparatively satisfactory.