A mathematical model for accident proneness

A new count model generated from mixed Poisson transmuted exponential family with an application to health care data

“…• Poisson-Gamma (Negative Binomial) - Greenwood and Yule (1920) • Poisson Beta with specific parameter values (Yule) - Simon (1955) • Poisson Beta Type-2 - Gurland (1958) • Poisson-Exponential Beta - Pielou (1962) • Poisson Truncated Poisson - Patil (1964) • Poisson Beta Type 1 -Holla and Bhattacharya (1965) • Poisson Truncated Gamma - Bhattacharya(1966) • Poisson Linear Exponential - Sankaran(1969) • Poisson Lindley - Sankaran (1970) • Poisson Power Function - Rai (1971) • Poisson Lognormal - Bulmer (1974) • Poisson Generalized Inverse Gaussian - Sichel (1974) • Poisson Inverse Gaussian - Sichel(1975) • Poisson Gamma Product Ratio(Generalized Waring) - Irwin (1975) • Poisson Generalized Pareto - Kempton (1975) • Poisson-Poisson Distribution(Neyman) - Douglas (1980) • Poisson Pearson's Family of Distribution - Albrecht (1982) • Poisson Generalized Gamma - Albrecht (1984) • Poisson Truncated Beta Type 2 - Willmot (1986) • Poisson Log-Student -Gover and O' Muircheartigh (1987) • Poisson Shifted Gamma -Ruhonen (1988) • Poisson Exponential(Geometric) - Johnson et al (1992) • Poisson-Other Discrete Distribution(Neyman) - Johnson et al (1992) • Poisson Linear Exponential - Kling and Goovaerts (1993) • Poisson Inverse Gamma - Willmot (1993) • Poisson Truncated Gamma - Willmot (1993) • Poisson Pareto - Willmot (1993) • Poisson Shifted Pareto - Willmot (1993) • Poisson Modified Bessel -Ong and Muthaloo (1995) The above monographs presents more flexible distributions as they can be used as building blocks for improving count data models. In the present paper, a new discrete distribution is obtained by mixing Poisson distribution with Transmuted-Exponential distribution proposed by Shaw and Buckley (2007).…”

“…• Poisson Beta with specific parameter values (Yule) - Simon (1955) • Poisson Beta Type-2 - Gurland (1958) • Poisson-Exponential Beta - Pielou (1962) • Poisson Truncated Poisson - Patil (1964) • Poisson Beta Type 1 -Holla and Bhattacharya (1965) • Poisson Truncated Gamma - Bhattacharya(1966) • Poisson Linear Exponential - Sankaran(1969) • Poisson Lindley - Sankaran (1970) • Poisson Power Function - Rai (1971) • Poisson Lognormal - Bulmer (1974) • Poisson Generalized Inverse Gaussian - Sichel (1974) • Poisson Inverse Gaussian - Sichel(1975) • Poisson Gamma Product Ratio(Generalized Waring) - Irwin (1975) • Poisson Generalized Pareto - Kempton (1975) • Poisson-Poisson Distribution(Neyman) - Douglas (1980) • Poisson Pearson's Family of Distribution - Albrecht (1982) • Poisson Generalized Gamma - Albrecht (1984) • The above monographs presents more flexible distributions as they can be used as building blocks for improving count data models. In the present paper, a new discrete distribution is obtained by mixing Poisson distribution with Transmuted-Exponential distribution proposed by Shaw and Buckley (2007).…”