Gráfico Q-Q modificado para grandes tamaños de muestra
A modified Q-Q plot for large sample sizes
Resumen (es)
El gráfico Q-Q es una herramienta para determinar si los datos observados se ajustan a una distribución de probabilidad teórica, en el que cada observación en los datos es representada por un símbolo. En muchas ocasiones, debido a variaciones naturales en los datos o un gran tamaño de muestra, el gráfico Q-Q puede interpretarse como una falla en el modelo probabilístico propuesto. Una alternativa es considerar un conjunto de características de los datos tales como los cuantiles muestrales que, en conjunto con su equivalente teórico, permitan al usuario comparar ambos de manera efectiva. Proponemos e ilustramos un gráfico Q-Q modificado que permite visualizar las diferencias entre los cuantiles observados y teóricos, y remediar algunas dificultades técnicas del gráfico tradicional.
Resumen (en)
The Q-Q plot is a graphical tool for assessing the fit of observed data to a theoretical distribution, in which every single observation in the data is represented by a symbol (usually a dot). In many occasions, due either to natural variations of the data or to a large sample size, the Q-Q plot could be interpreted as a sign of failure of the proposed model. An alternative is to consider a special set of characteristics of the data such as the sample quantiles that, jointly with its theoretical counterparts, allow the user to effectively compare both. We propose and illustrate a modified Q-Q plot that helps to visualise the differences between the observed quantiles and its corresponding theoretical values, and overcome some technical problems of the traditional Q-Q plot.
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