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Analysis of COVID-19 and cancer data using new half-logistic generated family of distributions

Khan Sadaf, Tahir Muhammad H., Jamal Farrukh

Operations Research and Decisions

2023

Vol. 33, No. 4

71--95

We focus on a specific sub-model of the proposed family that we call the new half logistic-Fréchet. This sub-model stems from a new generalisation of the half-logistic distribution which we call the new half-logistic-G. The novelty of proposing this new family is that it does not include any additional parameters and instead relies on the baseline parameter. Standard statistical formulas are used to show the forms of the density and failure rate functions, ordinary and incomplete moments with generating functions, and random variate generation. The maximum likelihood estimation procedure is used to estimate the set of parameters. We conduct a simulation analysis to ensure that our calculations are converging with lower mean square error and biases. We use three real-life data sets to equate our model to well-established existing models. The proposed model outperforms the well-established four parameters beta Fréchet and exponentiated generalized Fréchet for some real- -life results, with three parameters such as half-logistic Fréchet, exponentiated Fréchet, Zografos–Balakrishnan gamma Fréchet, Topp–Leonne Fréchet, and Marshall–Olkin Fréchet and two-parameter classical Fréchet distribution.

Maximum simulated likelihood: don't stop believin'?

Schrey Christopher

Annals of Computer Science and Information Systems

2021

Vol. 26

175--180

Unobserved heterogeneity may complicate model estimation in econometrics. To integrate out the effect of unobserved heterogeneity via maximum simulated likelihood (MSL) estimation, assumptions regarding the underlying distribution need to be made. Researchers seldomly discuss these assumptions. This raises the question, to what extent estimation results in the MSL-context are robust to potential distributional mismatch. This work-in-progress derives the research question from the literature. A simulation study is conducted that underpins the relevance of this matter, where results imply that mismatch may introduce significant bias. Intended future work to properly address and answer this question is defined and discussed.

Maximum simulated likelihood: Don’t stop ’til you get enough?

Schrey Christopher, Schäffer Tobias, Militzer-Horstmann Carsta, Kossack Nils

Annals of Computer Science and Information Systems

2019

Vol. 19

79--82

Maximum simulated likelihood estimation can be employed in empirical health economics, amongst others, to tackle issues concerning endogenous treatment effects. While theory suggests that maximum simulated likelihood estimation is asymptotically consistent, efficient and equivalent to the maximum likelihood estimator when both the number of simulation draws S and sample size N → ∞ and √N/S → 0 there is no guidance on how large of an S to choose and even theory suggests to experiment. This piece of research reviews strategies of health economists that aim at dealing with this issue. Most pieces of applied research rely on experimentation until numerical stability is achieved, while some employ Monte-Carlo techniques to justify their choice of S. A more formal test was suggested, but seemed not to be employed yet. This lack of guidance induces a research problem that needs to be properly addressed.