The Distribution of a Linear Combination of Two Correlated Chi-Square Variables
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| Format: | Artículo científico |
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Universidad Nacional de Colombia
2013
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| _version_ | 1876452613465047040 |
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| author | Anwar H. Joarder |
| author_facet | Anwar H. Joarder |
| contents | The Distribution of a Linear Combination of Two Correlated Chi-Square Variables Anwar H. Joarder M. Hafidz Omar Arjun K. Gupta Física, Astronomía y Matemáticas Moments Bivariate Chi Correlated Chi square Variables Linear Combination The distribution of the linear combination of two chi-square variables is known if the variables are independent. In this paper, we derive the distribution of positive linear combination of two chi-square variables when they are correlated through a bivariate chi-square distribution. Some properties of the distribution, namely, the characteristic function, cumulative distribution function, raw moments, mean centered moments, coefficients of skewness and kurtosis are derived. Results match with the independent case when the variables are uncorrelated. The graph of the density function is presented. 2013 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89929799002 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.36 |
| format | Artículo científico |
| id | redalyc_89929799002 |
| institution | Redalyc |
| language | en |
| publishDate | 2013 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | The Distribution of a Linear Combination of Two Correlated Chi-Square Variables Anwar H. Joarder Física, Astronomía y Matemáticas Moments Bivariate Chi Correlated Chi square Variables Linear Combination The Distribution of a Linear Combination of Two Correlated Chi-Square Variables Anwar H. Joarder M. Hafidz Omar Arjun K. Gupta Física, Astronomía y Matemáticas Moments Bivariate Chi Correlated Chi square Variables Linear Combination The distribution of the linear combination of two chi-square variables is known if the variables are independent. In this paper, we derive the distribution of positive linear combination of two chi-square variables when they are correlated through a bivariate chi-square distribution. Some properties of the distribution, namely, the characteristic function, cumulative distribution function, raw moments, mean centered moments, coefficients of skewness and kurtosis are derived. Results match with the independent case when the variables are uncorrelated. The graph of the density function is presented. 2013 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89929799002 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.36 |
| title | The Distribution of a Linear Combination of Two Correlated Chi-Square Variables |
| topic | Física, Astronomía y Matemáticas Moments Bivariate Chi Correlated Chi square Variables Linear Combination |
| url | https://www.redalyc.org/articulo.oa?id=89929799002 |