Comparación de intervalos de confianza obtenidos mediante aproximación normal y bootstrap para los parámetros de la Distribución Weibull
- Autores: Cesar Ojeda, Adriana Pereira Oviedo
- Localización: Comunicaciones en Estadística, ISSN 2027-3355, ISSN-e 2339-3076, Vol. 11, Nº. 1, 2018, págs. 63-75
- Idioma: español
- DOI: 10.15332/s2027-3355.2018.0001.03
- Títulos paralelos:
- Comparison of confidence intervals obtained by normal approximation and bootstrap for the Weibull distribution’s parameters
- Enlaces
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Resumen
- español
En este trabajo se analiza el desempeño de los métodos aproximación normal y bootstrap paramétrico para la estimación por intervalos de los parámetros de la distribución Weibull en dieciocho escenarios simulados, en los cuales bajo diferentes tamaños de muestra se valora el efecto del parámetro de forma $\beta$, en la estimación por intervalos para el parámetro de escala $\eta$ de la distribución Weibull, de igual manera se varía el parámetro de escala en la estimación por intervalos para el parámetro de forma. Se encuentra en los escenarios simulados que los intervalos de confianza construidos bajo aproximación bootstrap presentaron un mejor comportamiento que los obtenidos por aproximación normal en cuanto a la probabilidad de cobertura y longitud mediana. Los intervalos de confianza al $(1-\alpha)\times 100\%$ por aproximación normal para $\beta$ resultaron asimétricos con respecto al error $\alpha$. En ambos métodos de estimación se evidencia que para $\beta \geq 2$ los intervalos de confianza para el parámetro $\eta$ disminuyen la longitud.
- English
In this paper we analyze the performance of the confidence intervals estimation via normal approximation and parametric bootstrap for the parameters of the Weibull distribution in eighteen simulated scenarios. Under different sample sizes, the effect of the form parameter β on the interval estimate is evaluated for the scale parameter η. In the same way, the scale parameter is varied in the interval estimation for the shape parameter. We found that the confidence intervals constructed under the bootstrap approach show a better behavior in comparison with those obtained by normal approximation in terms of coverage probability and median length. The confidence intervals at (1 −α)×100 % by normal approximation for β were asymmetric with respect to the error α. In both methods, it is evident that for β ≥ 2 the confidence intervals for the parameter η decrease the length.
- español
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