Potencia y Robustez en Pruebas de Normalidad con Simulación Montecarlo

En esta investigación se planteó como objetivo general, examinar la potencia y robustez de las pruebas de normalidad en muestras grandes y pequeñas, generadas con simulación Montecarlo. Se aplicaron pruebas de hipótesis no paramétricas que miden el grado de discrepancia entre las distribuciones empíricas y la función de distribución acumulada normal, que analizan la correlación entre la distribución teórica y la experimental y las que se sustentan en el estudio de la asimetría y curtosis. La comparación se hizo en dos grupos con tamaño de muestras distintas. En las muestras grandes se compararon las pruebas de Kolmogorov-Smirnov; Chi-Cuadrado de Pearson; Jarque-Bera y Geary; en las muestras pequeñas Shapiro-Wilk; Cramér-von Mises; Lilliefors y Watson. Los contrastes se realizaron con el Programa informático RStudio y el criterio de rechazo para las hipótesis nulas se hizo a través del p-value. Como conclusión, la prueba de mayor robustez en muestras grandes es Kolmogorov estimándose que su probabilidad es menor a 0,11. En muestras pequeñas este resultado corresponde a Shapiro-Wilk con una estimación menor a 0,14. Con relación a la potencia en las pruebas de normalidad para muestras grandes se demostró que la más potente de ellas es la prueba Jarque Bera, con un intervalo de confianza entre 0,86 y 1. Para las muestras pequeñas ninguna de las pruebas sometidas a estudio resultó potente.

The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

Limit States of Structures and Global Sensitivity Analysis Based on Cramér-von Mises Distance

This article presents a stochastic computational model for the analysis of the reliability of a drawn steel bar. The whole distribution of the limit state function is studied using global sensitivity analysis based on Cramér-von Mises distance. The algorithm for estimating the sensitivity indices is based on one loop of the Latin Hypercube Sampling method in combination with numerical integration. The algorithm is effective due to the approximation of resistance using a threeparameter lognormal distribution. Goodness-of-fit tests and other comparative studies demonstrate the significant accuracy and suitability of the three-parameter lognormal distribution, which provides better results and faster response than sampling-based methods. Global sensitivity analysis is evaluated for two load cases with proven dominant effect of the long-term variation load action, which is introduced using Gumbel probability density function. The Cramér-von Mises indices are discussed in the context of other types of probability-oriented sensitivity indices whose performance has been studied earlier.

COMPUTER INFORMATION TECHNOLOGY FOR PROCESSING MEASUREMENTS IN THE TASKS OF MONITORING THE STATE OF TECHNICAL OBJECTS

The tasks of monitoring the state of complex technical objects are solved by evaluating and comparing experimental measurements. A new discrete analogue of the Smirnov-Cramer-von Mises criterion and a new discrete analogue of the Anderson criterion are proposed. Computational experiments have been carried out confirming the hypothesis that discrete models of the probability distribution function and the proposed discrete mean square of the difference in information content do not differ from the Anderson criterion and the Smirnov-Cramer-von Mises criterion, but it is much simpler in practical applications in the verification of statistical hypotheses homogeneity of short samples of experimental measurements.