Recurrence relations for bivariate and extended skew- distributions and an application to order statistics from bivariate
| Autor: | Narayanaswamy Balakrishnan, Yaser Mehrali, Ahad Jamalizadeh |
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| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Discrete mathematics Recurrence relation Applied Mathematics Cumulative distribution function Order statistic Degrees of freedom (statistics) Bivariate analysis Computational Mathematics Computational Theory and Mathematics Joint probability distribution Statistics High Energy Physics::Experiment Linear combination Mathematics t-statistic |
| Zdroj: | Computational Statistics & Data Analysis. 53:4018-4027 |
| ISSN: | 0167-9473 |
| Popis: | In this paper, we derive recurrence relations for cumulative distribution functions (cdf's) of bivariate t and extended skew-t distributions. These recurrence relations are over @n (the degrees of freedom), and starting from the known results for @n=1 and @n=2, they will allow for the recursive evaluation of the distribution function for any other positive integral value of @n. Then, we consider a linear combination of order statistics from a bivariate t distribution with an arbitrary mean vector and show that its cdf is a mixture of cdf's of the extended skew-t distributions. This mixture form, along with the explicit expressions of the cdf's of the extended skew-t distributions, enables us to derive explicit expressions for the cdf of the linear combination for any positive integral value of @n. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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