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ESTIMACIÓN POR INTERVALO DEL PARÁMETRO DE LA DISTRIBUCIÓN DE POISSON CON UNA SOLA OBSERVACIÓN
INTERVAL ESTIMATION FOR THE POISSON DISTRIBUTION PARAMETER WITH A SINGLE OBSERVATION
Keywords:
estimación, intervalo de confianza, tamaño de muestra pequeño, teorema central del límite, razón de verosimilitud (es)Estimation, Confidence interval, Small sample size, Central limit theorem, Likelihood ratio (en)
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1Escuela de Estadística, Universidad Nacional de Colombia, Medellín.
Profesor asociado. E-mail: jccorrea@unalmed.edu.co
La estimación del parámetro de la distribución de Poisson, digamos λ, es un problema importante en el trabajo estadístico aplicado. En muchas ocasiones solo disponemos de un único dato para construir un intervalo de confianza. Se muestra cuándo se pueden construir intervalos de confianza basados en el teorema central del límite, el método exacto y la razón de verosimilitud cuando se tiene una sola observación. Se ilustra este caso construyendo un intervalo para la tasa de suicidios en Colombia.
Palabras clave: estimación, intervalo de confianza, tamaño de muestra pequeño,teorema central del límite, razón de verosimilitud.
The estimation of the parameter of the Poisson distribution, say λ, is an important task in applied statistics. Frequently we only have available a single observation and our goal is to construct a confidence interval. We illustrate under what conditions we can construct a confidence interval based on three methods: central limit theorem, exact method, and the likelihood ratio method. We also illustrate this problem constructing a confidence interval for the rate of suicides in Colombia.
Key words: Estimation, Confidence interval, Small sample size, Central limit theorem, Likelihood ratio.
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Referencias
1. Billingsley, P. (1986), Probability and Measure, 2nd edn, John Wiley & Sons, New York.
2. Kalbfleish, J. G. (1985), Probability and Statistical Inference, Vol. 2, 2nd edn, Springer-Verlag, New York.
3. Lehmann, E. L. (1999), Elements of Large-Sample Theory, Springer-Verlag, New York.
4. Sarmiento, L. (2007), Jóvenes: ¿Por qué se suicidan?, Web, Red de Prensa No Alineados.[Internet]. http://www.voltairenet.org/image/article139303.html#article139303
5. Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, John Wiley, New York.
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