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# International Journal of Statistics and Applied Mathematics

#### 2020, Vol. 5, Issue 5, Part A

##### Comparison between weighted adjustment, diagonal adjustment, quasi optimization and Gibbs sampler methods in deriving the generator matrix of an $8\times 8$ credit transition matrix

Author(s): Fred Nyamitago Monari, Dr. Joseph Kyalo Mungatu, George Otieno Orwa and Romanus Odhiambo Otieno

Abstract:
A transition matrix P is said to be embeddable if it has a generator matrix Q such that P =exp (Q) If the approximated transition matrix P ̂ is embeddable, then the estimator Q ̂ can be got for the generator matrix Q. What of cases when P ̂ is not embeddable? This paper will show how to evaluate P ̂ and find estimatorˆin cases where is embeddable (Kingman, 1962). This problem can be solved by using four methods namely.
1. Diagonal and Weighted adjustments Method
2. The Generator Quasi-Optimization method
3. The EM logarithm Method
4. The Gibbs sampler (Markov Chain Monte Carlo Method)
Later after sampling each of the above methods, an L norm will be performed on the results so as to deduce which method is the best for estimating the Generator Matrix for an Credit transition Matrix.

Fred Nyamitago Monari, Dr. Joseph Kyalo Mungatu, George Otieno Orwa, Romanus Odhiambo Otieno. Comparison between weighted adjustment, diagonal adjustment, quasi optimization and Gibbs sampler methods in deriving the generator matrix of an $8\times 8$ credit transition matrix. Int J Stat Appl Math 2020;5(5):01-06.