Estimation of discrete mixed Poisson-Erlang distribution with applications to medical data

This paper discusses the estimation of the discrete mixed Poisson-Erlang distribution (DMPED). Compared to many traditional discrete distributions, DMPED offers several surprising benefits, especially when examining count data with high variation and that are positively skewed. We have explored several statistical characteristics of the assumed distribution, such as moments, the moment-generating function, the failure rate function, the monotonicity of the probability mass function, and a couple of descriptive measures (central tendency and dispersion). We have used the maximum likelihood estimation technique to estimate the parameters of the DMPED. We conducted a simulation study to validate the proposed estimators. Finally, four applications related to cancer diseases have been discussed, where DMPED (especially DMPEIID) fits the number of doses required for treatment, remission times, and therapy type comparisons.