| Summary: | 碩士 === 國立政治大學 === 應用數學系數學教學碩士在職專班 === 101 === If the given conditional distributions are compatible, then their corresponding joint distribution exists. In such case, we may be able to find its joint p.d.f. and to find maximum likelihood estimators of the parameters. However, when it is not easy to find the joint p.d.f. or the expression of the joint p.d.f. is too complicated, we may use the maximum pseudo-likelihood estimators to estimate the unknown parameters. In this thesis, using three different bivariate joint distributions, we study the difference between their maximum likelihood estimator (MLE) and maximum pseudo-likelihood estimator (MPLE) to find out if MPLE may replace MLE. These three distributions are Gumbel’s bivariate exponential distribution, bivariate normal distribution, and Marshall and Olkin’s bivariate exponential distribution. We find that MPLE’s and MLE’s are the same under Gumbel’s bivariate exponential distribution and bivariate normal distribution. However, it’s not possible that MPLE’s and MLE’s could be the same under Marshall and Olkin’s bivariate exponential distribution. In addition, through computer simulation study on Marshall and Olkin’s bivariate exponential distribution, we find that the difference between MPLE and MLE seems getting larger if the correlation coefficient is becoming larger. Finally, the derivation and/or computation of the MPLE for some distributions may be too complicated, even their MPLE’s and MLE’s are the same. Hence, it may not be worth of using MPLE, like the bivariate normal case. Therefore, we suggest finding out the joint p.d.f. first to estimate the parameters through MLE if it is possible, instead of using MPLE.
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