Some Inferential Problems from Log Student's T-distribution and its Multivariate Extension

• Autores: Akinlolu Olosunde, Sylvester Olofintuade
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 45, Nº. 1, 2022, págs. 209-229
• Idioma: inglés
• DOI: 10.15446/rce.v45n1.90672
• Títulos paralelos:
  • Algunos problemas inferenciales a partir de la distribución T de Student y su extension multivariante
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen La suposicion de normalidad en el analisis estadistico habia sido una pratica comun en mucha literatura, pero en el caso de que se pueda obtener una muestra pequena, la suposicion de normalidad conducira a conclusions erroneas en el analisis estadistico. En la practica, la toma de una muestra grande habia sido una gran preocupacion debido a varios factores. En este articulo, obtuvimos ademas algunas propiedades inferenciales para la distribucion t de log student (simplemente distribucion log-t) que la hace mas adecuada como sustituto de log-norma al realizar analisis en datos de muestras pequenas con sesgo a la derecha. Se derivan propiedades matematicas y estadisticas como los momentos, la funcion de supervivencia, la funcion de riesgo y la concavidad logaritmica. ampliamos aun mas el resultado al caso de distribucion log-t multivariante; obtuvimos las distribuciones marginales y condicionales. La estimacion de los parametros se realizo mediante el metodo de estimacion de maxima verosimilitud, por lo que se derivo su mejor region critica y matriz de informacion para obtener el intervalo de confianza asintotico. Las aplicaciones de la distribucion log-t y la prueba de bondad de ajuste se llevaron a cabo en dos conjuntos de datos de la literatura para mostrar cuando el modelo es mas apropiado.

  • English

    Abstract Assumption of normality in statistical analysis had been a common practice in many literature, but in the event where small sample is obtainable, then normality assumption will lead to erroneous conclusion in the statistical analysis. Taking a large sample had been a serious concern in practice due to various factors. In this paper, we further derived some inferential properties for log student's t-distribution (simply log-t distribution) which makes it more suitable as substitute to log-normal when carrying out analysis on right-skewed small sample data. Mathematical and Statistical properties such as the moments, cumulative distribution function, survival function, hazard function and log-concavity are derived. We further extend the results to case of multivariate log-t distribution; we obtained the marginal and conditional distributions. The parameters estimation was done via maximum likelihood estimation method, consequently its best critical region and information matrix were derived in order to obtain the asymptotic confidence interval. The applications of log-t distribution and goodness-of-fit test was carried out on two dataset from literature to show when the model is most appropriate.

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