Bivariate Zero-Inflated Power Series Distribution

ABSTRACT

Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defects, multivariate Poisson model is one of the appropriate model. This can further be modified to incorporate inflation at zero and we can have multivariate zero-inflated Poisson distribution. In the present article, we introduce a new Bivariate Zero Inflated Power Series Distribution and discuss inference related to the parameters involved in the model. We also discuss the inference related to Bivariate Zero Inflated Poisson Distribution. The model has been applied to a real life data. Extension to k-variate zero inflated power series distribution is also discussed.

Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defects, multivariate Poisson model is one of the appropriate model. This can further be modified to incorporate inflation at zero and we can have multivariate zero-inflated Poisson distribution. In the present article, we introduce a new Bivariate Zero Inflated Power Series Distribution and discuss inference related to the parameters involved in the model. We also discuss the inference related to Bivariate Zero Inflated Poisson Distribution. The model has been applied to a real life data. Extension to k-variate zero inflated power series distribution is also discussed.

KEYWORDS

Bivariate Zero-Inflated Power Series Distribution, Bivariate Zero-Inflated Poisson Distribution, K-Variate Zero-Inflated Power Series Distribution

Bivariate Zero-Inflated Power Series Distribution, Bivariate Zero-Inflated Poisson Distribution, K-Variate Zero-Inflated Power Series Distribution

Cite this paper

nullP. Krishna and S. Tukaram, "Bivariate Zero-Inflated Power Series Distribution,"*Applied Mathematics*, Vol. 2 No. 7, 2011, pp. 824-829. doi: 10.4236/am.2011.27110.

nullP. Krishna and S. Tukaram, "Bivariate Zero-Inflated Power Series Distribution,"

References

[1] L. Chin-Shang, K. Kyungmoo, J. P. Peterson and P. A. Brinkley, “Multivariate Zero-Inflated Poisson Models and Their Applications,” Technometrics, Vol. 41, No. 1, 1999, pp. 29-38. doi:10.2307/1270992

[2] S. R. Deshmukh and M. S. Kasture, “Bivariate Distribution with Truncated Poisson Marginal Distributions,” Communication in Statistics: Theory and Metords, Vol. 31, No. 4, 2002, pp. 527-534. doi:10.1081/STA-120003132

[3] P. L. Gupta and R. C. Tripathi, “Inflated Modified Power Series Distributions with Applications,” Communication in Statistics: Theory and Metords, Vol. 24, No. 9, 1995, pp. 2355-2374. doi:10.1080/03610929508831621

[4] R. L. Gupta and R. C. Tripathi “Score Test for Zero-Inflated Generalized Poisson Regression Model,” Communication in Statistics: Theory and Metords, Vol. 33, No. 1, 2004, pp. 47-64. doi: 10.1081/STA-120026576

[5] P. Holgate, “Estimation for the Bivariate Poisson Distribution,” Biometrika, Vol. 51, No. 1-2, 1964, pp. 241-245.

[6] D. Lambert, “Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing,” Technometrics, Vol. 34, No. 1, 1992, pp. 1-14. doi:10.2307/1269547

[7] J. Lakshiminarayana, S. N. N. Pandit and K. Srinivasa Rao, “On a Bivariate Poisson distribution,” Communication in Statistics: Theory and Metords, Vol. 28, No. 2, 1999, pp. 267-276.

[8] M. K. Patil and D. T. Shirke, “Testing Parameter of the Power Series Distribution of a Zero-Inflated Power Series Model,” Statistical Methodology, Vol. 4, No. 4, 2007, pp. 393-406. doi:10.1016/j.stamet.2006.12.001

[9] M. K. Patil and D. T. Shirke, “Tests for Equality of Inflation Parameters of Two Zero-Inflated Power Series Distributions,” Communications in Statistics: Theory and Methods, Vol. 40, No. 14, 2011, pp. 2539-2553. doi:10.1080/03610926.2010.489172

[10] A. G. Arbous and J. E. Kerrich, “Accident Statistics and the Concept of Accident Proneness,” Biometrics, Vol. 7, No. 1951, pp. 340-342. doi:10.2307/3001656

[1] L. Chin-Shang, K. Kyungmoo, J. P. Peterson and P. A. Brinkley, “Multivariate Zero-Inflated Poisson Models and Their Applications,” Technometrics, Vol. 41, No. 1, 1999, pp. 29-38. doi:10.2307/1270992

[2] S. R. Deshmukh and M. S. Kasture, “Bivariate Distribution with Truncated Poisson Marginal Distributions,” Communication in Statistics: Theory and Metords, Vol. 31, No. 4, 2002, pp. 527-534. doi:10.1081/STA-120003132

[3] P. L. Gupta and R. C. Tripathi, “Inflated Modified Power Series Distributions with Applications,” Communication in Statistics: Theory and Metords, Vol. 24, No. 9, 1995, pp. 2355-2374. doi:10.1080/03610929508831621

[4] R. L. Gupta and R. C. Tripathi “Score Test for Zero-Inflated Generalized Poisson Regression Model,” Communication in Statistics: Theory and Metords, Vol. 33, No. 1, 2004, pp. 47-64. doi: 10.1081/STA-120026576

[5] P. Holgate, “Estimation for the Bivariate Poisson Distribution,” Biometrika, Vol. 51, No. 1-2, 1964, pp. 241-245.

[6] D. Lambert, “Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing,” Technometrics, Vol. 34, No. 1, 1992, pp. 1-14. doi:10.2307/1269547

[7] J. Lakshiminarayana, S. N. N. Pandit and K. Srinivasa Rao, “On a Bivariate Poisson distribution,” Communication in Statistics: Theory and Metords, Vol. 28, No. 2, 1999, pp. 267-276.

[8] M. K. Patil and D. T. Shirke, “Testing Parameter of the Power Series Distribution of a Zero-Inflated Power Series Model,” Statistical Methodology, Vol. 4, No. 4, 2007, pp. 393-406. doi:10.1016/j.stamet.2006.12.001

[9] M. K. Patil and D. T. Shirke, “Tests for Equality of Inflation Parameters of Two Zero-Inflated Power Series Distributions,” Communications in Statistics: Theory and Methods, Vol. 40, No. 14, 2011, pp. 2539-2553. doi:10.1080/03610926.2010.489172

[10] A. G. Arbous and J. E. Kerrich, “Accident Statistics and the Concept of Accident Proneness,” Biometrics, Vol. 7, No. 1951, pp. 340-342. doi:10.2307/3001656