2008, Vol. 32, Núm. 1 http://hdl.handle.net/2099/8906 2019-08-23T22:12:46Z A note on the likelihood and moments of the skew-normal distribution http://hdl.handle.net/2099/8944 A note on the likelihood and moments of the skew-normal distribution Martínez, E. H.; Varela, H.; Gómez, H. W.; Bolfarine, Heleno 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. 2010-04-27T14:41:36Z Martínez, E. H. Varela, H. Gómez, H. W. Bolfarine, Heleno 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 interval estimation for the mean of inverse Gaussian distribution http://hdl.handle.net/2099/8943 A note on interval estimation for the mean of inverse Gaussian distribution Arefi, M.; Mohtashami Borzadaran, G.R.; Vaghei, Y. In this paper, we study the interval Estimation for the mean from inverse Gaussian distribution. This distribution is a member of the natural exponential families with cubic variance function. Also, we simulate the coverage probabilities for the confidence intervals considered. The results show that the likelihood ratio interval is the best interval and Wald interval has the poorest performance. 2010-04-27T14:39:43Z Arefi, M. Mohtashami Borzadaran, G.R. Vaghei, Y. In this paper, we study the interval Estimation for the mean from inverse Gaussian distribution. This distribution is a member of the natural exponential families with cubic variance function. Also, we simulate the coverage probabilities for the confidence intervals considered. The results show that the likelihood ratio interval is the best interval and Wald interval has the poorest performance. An alternative analysis of variance http://hdl.handle.net/2099/8942 An alternative analysis of variance Longford, Nicholas T. The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative. 2010-04-27T14:39:21Z Longford, Nicholas T. The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative. Canonical non-symmetrical correspondence analysis: an alternative in constrained ordination http://hdl.handle.net/2099/8941 Canonical non-symmetrical correspondence analysis: an alternative in constrained ordination Willems, P. M.; Galindo Villardon, Ma. Purificación Canonical non-symmetrical correspondence analysis is developed as an alternative method for constrained ordination, relating external information (e.g., environmental variables) with ecological data, considering species abundance as dependant on sites. Ordination axes are restricted to be linear combinations of the environmental variables, based on the information of the most abundant species. This extension and its associated unconstrained ordination method are terms of a global model that permits an empirical evaluation of the impact that the environmental variables have on the community composition. Scores, contributions, qualities of representation, interpretation of dispersion graphs and an application to real vegetation data are presented. 2010-04-27T14:38:55Z Willems, P. M. Galindo Villardon, Ma. Purificación Canonical non-symmetrical correspondence analysis is developed as an alternative method for constrained ordination, relating external information (e.g., environmental variables) with ecological data, considering species abundance as dependant on sites. Ordination axes are restricted to be linear combinations of the environmental variables, based on the information of the most abundant species. This extension and its associated unconstrained ordination method are terms of a global model that permits an empirical evaluation of the impact that the environmental variables have on the community composition. Scores, contributions, qualities of representation, interpretation of dispersion graphs and an application to real vegetation data are presented. Empirical comparison between the Nelson-Aalen Estimator and the Naive Local Constant Estimator http://hdl.handle.net/2099/8940 Empirical comparison between the Nelson-Aalen Estimator and the Naive Local Constant Estimator Pérez Marín, Ana María The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guill ´en, Nielsen and P´erez-Mar´ın, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out. In this paper the efficiency performance of these two estimators when applied to real survival data are compared. Our results suggest that the efficiency improvement introduced by the naive local constant estimator is highly remarkable for all distribution quantiles, especially for low quantiles. 2010-04-27T14:37:42Z Pérez Marín, Ana María The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guill ´en, Nielsen and P´erez-Mar´ın, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out. In this paper the efficiency performance of these two estimators when applied to real survival data are compared. Our results suggest that the efficiency improvement introduced by the naive local constant estimator is highly remarkable for all distribution quantiles, especially for low quantiles. Construction of multivariate distributions: a review of some recent results http://hdl.handle.net/2099/8930 Construction of multivariate distributions: a review of some recent results Sarabia Alzaga, José María; Gómez Déniz, Emilio The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables in common and (f) Other methods, which include multivariate weighted distributions, vines and multivariate Zipf distributions. 2010-04-26T12:11:23Z Sarabia Alzaga, José María Gómez Déniz, Emilio The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables in common and (f) Other methods, which include multivariate weighted distributions, vines and multivariate Zipf distributions.