Modelo unibimodal simétrico-asimétrico con
aplicación al estudio del RNA VIH-1

GUILLERMO MARTÍNEZ-FLÓREZ^a, GERMÁN MORENO-ARENAS^b,
^a Universidad de Córdoba, Departamento de Matemáticas y Estadística, Montería, Colombia.
^b Universidad Industrial de Santander, Escuela de Matemáticas, Bucaramanga, Colombia.

Resumen Se definen dos nuevas distribuciones de probabilidad: modelo unibimodal simétrico con función de riesgo proporcional a la distribución normal y modelo unibimodal asimétrico con función de riesgo proporcional a la distribución normal asimétrica. Estos modelos permiten ajustar datos censurados con comportamiento bimodal y altos (o bajos) niveles de curtosis comparado con la curtosis de la distribución normal y altos (o bajos) niveles de asimetría. Además, se estiman los parámetros de los modelos por máxima verosimilitud y se determina la matriz de información observada. La flexibilidad de la nueva distribución se ilustra ajustando un conjunto de datos reales: el número de moléculas de ARN VIH-1 por mililitros de sangre medida en personas con pruebas confirmadas de presencia del VIH.

Palabras claves: Bimodalidad, asimetría, curtosis, función de riesgo proporcional, censura, límite de detección, ARN VIH-1, HAART.
MSC2010: 62F10, 62F12, 62N86

Uni-bimodal Symmetric-Asymmetric Model with
Application to the Study of HIV-1 RNA

Abstract We define two new probability distributions, unibimodal symmetric model with proportional hazard function to the normal distribution and unibimodal asymmetric model with proportional hazard function to the skewnormal distribution. These models allow adjust censored data with bimodal behavior and high (or low) levels of kurtosis compared with kurtosis of the normal distribution and high (or low) levels of asymmetry. The model parameters are estimated by maximum likelihood and the observed information matrix is determined. The flexibility of the new distribution is illustrated by adjusting a set of real data, the number of molecules of HIV-1 RNA per milliliter of blood measured in individuals with confirmed test of the presence of HIV.

Keywords: Bimodality, skewness, kurtosis, proportional hazard function, censorship, limit of detection, HIV-1 RNA, HAART.

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^*Autor para correspondencia: E-mail: gmorenoa@uis.edu.co
Recibido: 29 de enero de 2013, Aceptado: 03 de febrero de 2014.
Para citar este artículo: G. Martínez-Flórez, G. Moreno-Arenas, Modelo unibimodal simétrico-asimétrico
con aplicación al estudio del RNA VIH-1, Rev. Integr. Temas Mat. 32 (2014), no. 1, 1-18.