### Abstract

In this chapter the authors set the guidelines to approach cases not covered by the finite form representations studied in the book, give new Mellin inversion formulas for both the p.d.f. and the c.d.f., and develop sharp upper bounds on the difference between the exact and approximate representations for the Meijer G functions as well as for the differences between the exact and approximate p.d.f.’s and c.d.f.’s of the product of independent Beta r.v.’s.

Original language | English |
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Title of host publication | Finite Form Representations for Meijer G and Fox H Functions |

Place of Publication | Cham |

Publisher | Springer |

Pages | 491-505 |

Number of pages | 15 |

ISBN (Electronic) | 978-3-030-28790-0 |

ISBN (Print) | 978-3-030-28789-4 |

DOIs | |

Publication status | Published - 2019 |

### Publication series

Name | Lecture Notes in Statistics |
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Publisher | Springer |

Volume | 223 |

ISSN (Print) | 0930-0325 |

ISSN (Electronic) | 2197-7186 |

### Keywords

- Alternative approaches
- Near-exact distributions
- Other cases
- Simulation

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## Cite this

Coelho, C. A., & Arnold, B. C. (2019). Approximate finite forms for the cases not covered by the finite representation approach. In

*Finite Form Representations for Meijer G and Fox H Functions*(pp. 491-505). (Lecture Notes in Statistics; Vol. 223). Cham: Springer. https://doi.org/10.1007/978-3-030-28790-0_7