A Note on Efficient Computation for Information Matrix of Phase-Type Distribution

摘要

The PH expansion is an approximate method to an-alyze the model involving general distributions. Theidea of PH expansion is to use PH distribution insteadof general distribution in the model. The PH distribu-tion is the distribution of absorbing time of a CTMCwith absorbing state. It is known that PH distribu-tion can approximate any distribution with high accu-racy. In general, the variance of estimated parameterscan be computed by the Fisher's information matrix.However, the information matrix requires the secondderivative of log-likelihood function. Since PH distri-bution consists of many parameters, computation ef-forts for the second derivatives of log-likelihood func-tion is not so low. In this paper, we focus on the effi-cient computation of information matrix for PH distri-butions.