Poisson Transmuted Exponential Distribution For Count Data With Skewed, Dispersed And Excess Zero - Ademola Abiodun, Adetunji (2024)
Assuming Poisson Distribution For Count Data May Be Misleading In Most Cases Because It Assumes Equidispersion, Whereas Count Data Is Usually Overdispersed. In Actuarial Science, Claim Frequencies Are Usually Unimodal, Skewed, Overdispersed, And With A Higher Frequency Of Zero Counts; Hence, Assuming The Poisson Distribution May Lead To Model Misspecification. This Study Expands Theories And Scopes Of Discrete Distributions For Skewed And Overdispersed Count Observations With Excess Zero Frequency In The Mixed Poisson Process By Leveraging Extended Exponential Distributions' Unimodality And Skewness Properties. Three Transmutation Maps Are Used To Extend The Exponential Distributions, The Weighted Exponential Distribution, And The New Weighted Exponential Distribution. The Obtained Distributions Are Assumed As Mixing Distributions For The Parameter Of The Poisson Distribution In The Mixed Poisson Process. Nine New Mixed Poisson Distributions And Their Respective Zero-Inflated Forms Are Proposed From These Mixing Distributions. Different Moment-Based Mathematical Properties Of The New Proposed Distributions Are Obtained. Different Algorithms Are Used To Assess The Maximum Likelihood Estimates For The Parameters Of The Proposed Distributions.The Newton-Raphson And The Nelder-Mead, With Minimum Iterations For Convergence And Log-Likelihood Values, Provide Optimum Estimates. The New Proposed Distributions Are Assessed With Other Discrete Distributions On Various Real-Life Dispersed Count Observations With Excess Zero. The New Proposed Distributions Perform Well In Diverse Scenarios And Can Be Better Alternatives To Analyzing Overdispersed Count Observations With Excess Zero.