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This paper introduces a basic methodology which, based on simulations, determines the mínimum sample size necessary to use the normal approximation when estimating means from population with bounded symmetric distributions.

Tipo de documento: Artículo - Article

Palabras clave: Estadística matemática, Teoría de la distribución, Estimación de la distribución simétrica, Relación de equivalencia, Simulac ión de Montecarlo, Distribución triangular, Estadística matemática, Teoría de la distribución

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## Teaser

Revista Colombiana de Estadística No.
31 y No.
32 NORMAL APPROXIMATION WHEN SAMPLING FROM BOUNDED SYMMETRIC DISTRIBUTIONS JAIRO CLAVIJO M. Department of Mathematics Universidad del Toüma Ibagué, Colombia DAVID OSPINA Department of Mathematics and Statistics Universidad Nacional de Colombia Santafé de Bogotá, Colombia K E Y WORDS AND PHRASES; Bounded sysmietric distribution; equivalence relation; Finucans prindple; kurtosis; Monte Cario simulation; nonnal approximation; sample sise; triangular distribution; Van Zweets ordering. ABSTRACT.
This paper introduces a baaic methodology which, based on simulations, determines the mínimum s a n ó l e size neceasary to use the normal approximation when estimating meana from populationa with bounded symmetric distributions. 1. INTRODUCTION The sample siie is a crucial aspect of statistical research since it must be large enough to guarantee the prefíxed confidence level for the estimations and as small as possible to minimize the costs. The determination of samiple size is a probiem of difficult solution using analytic methods.
Generally, researchers make use of the central limit theorem, the law of laurge numbers or the Chcbychev inequaUty.
However, in mamy cases the values obtadned with these methods are laage and the budget assigned to the study is too smadl to satisfy them.
Financial restrictions are, usually, the main reason to look for new procedures. In this article, some mathematical results, derived from weU-known generad concepts, as well as certain simulation techniques, are used to deternúne those mínima Typeset by AM^-TpX 24 CLAVIJO JAIRO A.
AND OSPINA DAVID valúes that support the normal approximation in the estimation process of means for bounded symmetric distributions.
The final results show the convenience of the methodology used which could be implemented with other problems of similar caracteristics. 2.
PRELIMINARY THEORY For theoretical convenience this paper has been oriented to ...