The aim of this paper is the derivation of the maximum likelihood estimators of the Marshal-Olkin copula. This copula comes from the Marshall-Olkin Bivariate Exponential (MOBE) distribution, that has been proposed in reliability analysis to study complex systems in which the components are not independent and it is also used in the extreme value theory. We find the likelihood estimators conside...

.............................................................................................................................................................................. 2 Introduction ......................................................................................................................................................................... 2 Materials and methods ................

The Zipf distribution also known as scale-free distribution or discrete Pareto distribution, is the particular case of Power Law distribution with support the strictly positive integers. It is a one-parameter distribution with a linear behaviour in the log-log scale. In this paper the Zipfian distribution is generalized by means of the Marshall-Olkin transformation. The new model has more flexi...

This Internet Appendix presents material that is supplemental to the main analysis and tables in “Firm Level Productivity, Risk, and Return.”We supplement the empirical analysis in the paper with details on the measurement of TFP, detailed description of data, additional properties of TFP, and empirical robustness checks. We supplement the theoretical analysis with a figure to illustrate the mo...

A dual class of the multivariate distributions of Marshall-Olkin type is introduced, and their copulas are presented and utilized to derive explicit expressions of the distributional tail dependencies, which describe the amount of dependence in the upperorthant tail or lower-orthant tail of a multivariate distribution and can be used in the study of dependence among extreme values. A sufficient...

gional Laboratory Medicine Program, Hamilton (Dr Lee). Correspondence: Dr Lee, St Joseph’s Healthcare, 50 Charlton Ave E, Room L424, Hamilton, ON L8N 4A6, Canada ([email protected]). Author Contributions: Study concept and design: Kassam, Hundal, and Lee. Acquisition of data: Kassam, Hundal, and Lee. Analysis and interpretation of data: Kassam, Hundal, Marshall, and Lee. Drafting of the manuscri...

OBJECTIVE To analyze the effectiveness of the Marshall scoring system to evaluate the severity of acute pancreatitis (AP). METHODS We performed a prospective, observational study in 39 patients with AP evaluated by the Marshall scoring system and the Ranson criteria (admission and 48 hours). We assessed the progression of the disease for seven days and compared the data of the two criteria. ...