Application of a Markovian process to the calculation of mean time equilibrium in a genetic drift model

The most common phenomena in the evolution process are natural selection and genetic drift. In this article, we propose a probabilistic method to calculate the mean and variance time for random genetic drift equilibrium, measured as number of generations, based on Markov process and a complex probabilistic model. We studied the case of a constant, panmictic population of diploid organisms, which had a demonstrated lack of mutation, selection or migration for a determined autonomic locus, and two possible alleles, H and h. The calculations presented in this article were based on a Markov process. They explain how genetic and genotypic frequencies changed in different generations and how the heterozygote alleles became extinguished after many generations. This calculation could be used in more evolutionary applications. Finally, some simulations are presented to illustrate the theoretical calculations presented using different basal situations.     

Optimizing the test power for a radiation retention model in the human body

The model that describes the retention in lungs of radioisotope particles is studied in this paper, considering the situation of an accident in facilities that handle radioactive materials. Optimal times to make the bioassays are computed for D‐ and c‐optimality, and efficiencies for the computed designs are provided and compared. Moreover, the test power is checked by means of simulations and replications. After that the inverse of the Fisher information matrix is compared to an estimation of the covariance matrix of the parameters. Finally, a study taking into consideration the randomness of the designs space is performed. Copyright © 2009 John Wiley & Sons, Ltd.     

The Effects of Transformational Leadership on Organizational Performance through Knowledge and Innovation*

Today's information and knowledge society requires new leaders who can confront a reality based on knowledge and foster innovation to achieve improvements in organizational performance. However, organizations sometimes fail to achieve sustainable competitive advantage due to their limited understanding of the relationships between these strategic variables. To date, very little research has analysed the direct and indirect relationships between these variables. Our study seeks to fill this research gap by analysing theoretically and empirically how the leader's perceptions of different intermediate strategic variables related to knowledge (knowledge slack, absorptive capacity, tacitness, organizational learning) and innovation influence the relation between transformational leadership and organizational performance. Based on the literature, we develop a theoretical model that shows the interrelations between these variables. We then test the model using data from 408 Spanish organizations, discuss the findings and provide several implications for business practitioners.     

Finite sample performance of frequency- and time-domain tests for seasonal fractional integration

Testing the order of integration of economic and financial time series has become a conventional procedure prior to any modelling exercise. In this paper, we investigate and compare the finite sample properties of the frequency-domain tests proposed by Robinson [Efficient tests of nonstationary hypotheses, J. Amer. Statist. Assoc. 89(428) (1994), pp. 1420–1437] and the time-domain procedure proposed by Hassler, Rodrigues, and Rubia [Testing for general fractional integration in the time domain, Econometric Theory 25 (2009), pp. 1793–1828] when applied to seasonal data. The results presented are of empirical relevance as they provide some guidance regarding the finite sample properties of these tests.     

On the Smoothness of Projections in Statistical Models

Here we examine the existence of the projection of a probability measure in a parametric statistical model. Once, in a general framework, the existence of the projection is established, we consider the problem from a statistical point of view, modeling a parametric statistical model as a convenient manifold.     

Prior Density Selection as a Particular Case of Bayesian Model Selection: A Predictive Approach

A Bayesian model consists of two elements: a sampling model and a prior density. The problem of selecting a prior density is nothing but the problem of selecting a Bayesian model where the sampling model is fixed. A predictive approach is used through a decision problem where the loss function is the squared L ² distance between the sampling density and the posterior predictive density, because the aim of the method is to choose the prior that provides a posterior predictive density as good as possible. An algorithm is developed for solving the problem; this algorithm is based on Lavine's linearization technique.     

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967 Jeffreys , H. ( 1967 ). Theory of Probability , 3rd rev. ed. . London : Oxford University Press . [Google Scholar]), Lindley (1956 Lindley , D. V. ( 1956 ). On a measure of the information provided by an experiment . Ann. Mathemat. Statist. 27 : 986 – 1005 .[Crossref] , [Google Scholar]); (1961 Lindley , D. V. ( 1961 ). The use of prior probability distributions in statistical inference and decisions . In: Neyman , J. , ed. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability . Vol. 1. Berkeley : University of California Press , pp. 453 – 468 . [Google Scholar]), Hartigan (1964 Hartigan , J. ( 1964 ). Invariant priors distributions . Ann. Mathemat. Statist. 35 : 836 – 845 .[Crossref] , [Google Scholar]), Bernardo (1979 Bernardo , J. M. ( 1979 ). Reference posterior distributions for Bayesian inference . J. Roy. Statist. Soc. 41 ( 2 ): 113 – 147 . [Google Scholar]), Zellner (1984 Zellner , A. ( 1984 ). Maximal Data Information Prior Distributions, Basic Issues in Econometrics . Chicago : University of Chicago Press . [Google Scholar]), Tibshirani (1989 Tibshirani , R. ( 1989 ). Noninformative priors for one parameters of many . Biometrika 76 : 604 – 608 .[Crossref], [Web of Science ®] , [Google Scholar]), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984 Zellner , A. ( 1984 ). Maximal Data Information Prior Distributions, Basic Issues in Econometrics . Chicago : University of Chicago Press . [Google Scholar]), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.     

A Goodness-of-Fit Test for the Gumbel Distribution Based on Kullback–Leibler Information

A goodness-of-fit test for the Gumbel distribution is proposed. This test is based on the Kullback–Leibler discrimination information methodology proposed by Song (2002 Song , K. S. ( 2002 ). Goodness-of-fit tests based on Kullback–Leibler discrimination information . IEEE Trans. Inform. Theor. 48 : 1103 – 1117 .[Crossref], [Web of Science ®] , [Google Scholar]). The critical values of the test were obtained by using Monte Carlo simulation for small sample sizes and different levels of significance. The proposed test is compared with the tests developed by Stephens (1977 Stephens , M. ( 1977 ). Goodness-of-fit tests for the extreme value distribution . Biometrika 65 : 730 – 737 . [Google Scholar]), Chandra et al. (1981 Chandra , M. , Singpurwalla , N. D. , Stephens , M. A. ( 1981 ). Kolmogorov statistics for tests of fit for the extreme value and Weibull distributions . J. Amer. Statist. Assoc. 74 : 729 – 735 . [Google Scholar]), and the test given by Kinnison (1989 Kinnison , R. (1989). Correlation coefficient goodness of fit test for the extreme value distribution. Amer. Statistician 43:98–100.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in terms of their power by considering various alternative distributions. Simulation results show that the Kullback–Leibler information test has higher power than some of the studied tests.     

Multivariate Three-Parameter Log-Elliptical Distributions

The three-parameter log-elliptical distribution class is developed for the general situation in which the hypothesis of independence for the elements in a sample is not assumed. The parameter estimators are theoretically showed to be invariant under all distributions in the class by considering only a change in the constant of the scale parameter estimator. An estimation procedure based on the three-parameter lognormal distribution is proposed for the parameter estimation problem in any three-parameter log-elliptical distribution. Two classical lognormal data sets are analyzed without assuming independence in the sample in order to illustrate the proposed estimation procedure.