A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.Peer Reviewe

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting

Round Table: 30 years of ABEI and 10 years of WB Yeats Chair of Irish Studies

The round table commemorating the thirtieth anniversary of the BrazilianAssociation of Irish Studies (ABEI) and tenth year of the W.B. Yeats Chair of Irish Studies was part of the XIV ABEI and II AEIS Symposium of Irish Studies - “The State of the Art: Local and Global Contexts in Dialogue”, and was held on August 15, 2019. The session was comprised by Dr Munira H. Mutran, honorary president of ABEI and director of the W.B. Yeats Chair of Irish Studies; Dr Laura P.Z. de Izarra, coordinator of the W.B. Yeats Chair and advisory member of ABEI; Dr Rosalie R. Haddad, advisory member of ABEI and researcher in the W.B. Yeats Chair, Alessandra Cristina Rigonato, PhD candidate at the University ofSão Paulo, and Eduardo Kumamoto, graduate from the University of São Paulo and Master in Literary Translation at Trinity College Dublin. The discussion, which revolved around the history of the founding of both ABEI and the Chair, and their current developments, was conducted by Dr Mariana Bolfarine, head of ABEI and researcher at the W.B. Yeats Chair of Irish Studies

Should adjustment for covariates be used in prevalence estimations?

Background Adjustment for covariates (also called auxiliary variables in survey sampling literature) is commonly applied in health surveys to reduce the variances of the prevalence estimators. In theory, adjusted prevalence estimators are more accurate when variance components are known. In practice, variance components needed to achieve the adjustment are unknown and their sample estimators are used instead. The uncertainty introduced by estimating variance components may overshadow the reduction in the variance of the prevalence estimators due to adjustment. We present empirical guidelines indicating when adjusted prevalence estimators should be considered, using gender adjusted and unadjusted smoking prevalence as an illustration. Methods We compare the accuracy of adjusted and unadjusted prevalence estimators via simulation. We simulate simple random samples from hypothetical populations with the proportion of males ranging from 30% to 70%, the smoking prevalence ranging from 15% to 35%, and the ratio of male to female smoking prevalence ranging from 1 to 4. The ranges of gender proportions and smoking prevalences reflect the conditions in 1999–2003 Behavioral Risk Factors Surveillance System (BRFSS) data for Massachusetts. From each population, 10,000 samples are selected and the ratios of the variance of the adjusted prevalence estimators to the variance of the unadjusted (crude) ones are computed and plotted against the proportion of males by population prevalence, as well as by population and sample sizes. The prevalence ratio thresholds, above which adjusted prevalence estimators have smaller variances, are determined graphically. Results In many practical settings, gender adjustment results in less accuracy. Whether or not there is better accuracy with adjustment depends on sample sizes, gender proportions and ratios between male and female prevalences. In populations with equal number of males and females and smoking prevalence of 20%, the adjusted prevalence estimators are more accurate when the ratios of male to female prevalences are above 2.4, 1.8, 1.6, 1.4 and 1.3 for sample sizes of 25, 50, 100, 150 and 200, respectively. Conclusion Adjustment for covariates will not result in more accurate prevalence estimator when ratio of male to female prevalences is close to one, sample size is small and risk factor prevalence is low. For example, when reporting smoking prevalence based on simple random sampling, gender adjustment is recommended only when sample size is greater than 200