Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 50, Issue 13, Pages 3030-3050Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2019.1679182
Keywords
Poisson distribution; skew normal distribution; maximum likelihood estimators; EM type algorithm; Fisher information matrix; 62E15; 62F10; 62H10
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Funding
- University of Jordan
- DSR
- Science and Engineering Research Board, Government of India
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This study introduces a compound zero-truncated Poisson normal distribution and a four-parameter bivariate distribution with continuous and discrete marginals. It discusses estimation of unknown parameters using an EM type algorithm, and assesses the effectiveness of the algorithm through simulation experiments and analysis of a real data set.
Here, we first propose three-parameter model and call it as the compound zero-truncated Poisson normal (ZTP-N) distribution. The model is based on the random sum of N independent Gaussian random variables, where N is a zero truncated Poisson random variable. The proposed ZTP-N distribution is a very flexible probability distribution function. The probability density function can take variety of shapes. It can be both positively and negatively skewed, moreover, normal distribution can be obtained as a special case. It can be unimodal, bimodal as well as multimodal also. It has three parameters. An efficient EM type algorithm has been proposed to compute the maximum likelihood estimators of the unknown parameters. We further propose a four-parameter bivariate distribution with continuous and discrete marginals, and discuss estimation of unknown parameters based on the proposed EM type algorithm. Some simulation experiments have been performed to see the effectiveness of the proposed EM type algorithm, and one real data set has been analyzed for illustrative purposes.
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