Linking the Negative Binomial and Logarithmic Series Distributions via their Associated Series
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| Format: | Artículo científico |
| Language: | en |
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Universidad Nacional de Colombia
2008
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| author | Mauricio Sadinle |
| author_facet | Mauricio Sadinle |
| contents | Linking the Negative Binomial and Logarithmic Series Distributions via their Associated Series Mauricio Sadinle Física, Astronomía y Matemáticas Convergent series power series distributions logarithmic seriesdistribution negative binomial distribution The negative binomial distribution is associated to the series obtained by taking derivatives of the logarithmic series. Conversely, the logarithmic series distribution is associated to the series found by integrating the series associated to the negative binomial distribution. The parameter of the number of failures of the negative binomial distribution is the number of derivatives needed to obtain the negative binomial series from the logarithmicseries. The reasoning in this article could be used as an alternative method to prove that the probability mass function of the negative binomial distribution sums to one. Finally, an interpretation of the logarithmic series distribution is given by using the presented reasoning. 2008 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89912222011 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.2 Vol.31 |
| format | Artículo científico |
| id | redalyc_89912222011 |
| language | en |
| publishDate | 2008 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | Linking the Negative Binomial and Logarithmic Series Distributions via their Associated Series Mauricio Sadinle Física, Astronomía y Matemáticas Convergent series power series distributions logarithmic seriesdistribution negative binomial distribution Linking the Negative Binomial and Logarithmic Series Distributions via their Associated Series Mauricio Sadinle Física, Astronomía y Matemáticas Convergent series power series distributions logarithmic seriesdistribution negative binomial distribution The negative binomial distribution is associated to the series obtained by taking derivatives of the logarithmic series. Conversely, the logarithmic series distribution is associated to the series found by integrating the series associated to the negative binomial distribution. The parameter of the number of failures of the negative binomial distribution is the number of derivatives needed to obtain the negative binomial series from the logarithmicseries. The reasoning in this article could be used as an alternative method to prove that the probability mass function of the negative binomial distribution sums to one. Finally, an interpretation of the logarithmic series distribution is given by using the presented reasoning. 2008 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89912222011 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.2 Vol.31 |
| title | Linking the Negative Binomial and Logarithmic Series Distributions via their Associated Series |
| topic | Física, Astronomía y Matemáticas Convergent series power series distributions logarithmic seriesdistribution negative binomial distribution |
| url | https://www.redalyc.org/articulo.oa?id=89912222011 |