### Abstract

The univariate inverse trinomial distribution is so named because its cumulant generating function (c.g.f.) is the inverse of the c.g.f. of a trinomial distribution. The inverse trinomial distribution, which includes the inverse binomial and negative binomial distributions, is derivable from the Lagrangian expansion. The present paper pertains to the definition of the bivariate and multivariate inverse trinomial distributions through Lagrangian probability distributions. A multivariate inverse binomial distribution, generated by the method of reduction, converges to a multivariate inverse Gaussian distribution as a limiting form.

Original language | English |
---|---|

Pages (from-to) | 1585-1598 |

Number of pages | 14 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 26 |

Issue number | 7 |

Publication status | Published - 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality
- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*26*(7), 1585-1598.

**Multivariate inverse trinomial distribution as a Lagrangian probability model.** / Shimizu, Kunio; Nishii, Nobuharu; Minami, Mihoko.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 26, no. 7, pp. 1585-1598.

}

TY - JOUR

T1 - Multivariate inverse trinomial distribution as a Lagrangian probability model

AU - Shimizu, Kunio

AU - Nishii, Nobuharu

AU - Minami, Mihoko

PY - 1997

Y1 - 1997

N2 - The univariate inverse trinomial distribution is so named because its cumulant generating function (c.g.f.) is the inverse of the c.g.f. of a trinomial distribution. The inverse trinomial distribution, which includes the inverse binomial and negative binomial distributions, is derivable from the Lagrangian expansion. The present paper pertains to the definition of the bivariate and multivariate inverse trinomial distributions through Lagrangian probability distributions. A multivariate inverse binomial distribution, generated by the method of reduction, converges to a multivariate inverse Gaussian distribution as a limiting form.

AB - The univariate inverse trinomial distribution is so named because its cumulant generating function (c.g.f.) is the inverse of the c.g.f. of a trinomial distribution. The inverse trinomial distribution, which includes the inverse binomial and negative binomial distributions, is derivable from the Lagrangian expansion. The present paper pertains to the definition of the bivariate and multivariate inverse trinomial distributions through Lagrangian probability distributions. A multivariate inverse binomial distribution, generated by the method of reduction, converges to a multivariate inverse Gaussian distribution as a limiting form.

UR - http://www.scopus.com/inward/record.url?scp=0031361863&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031361863&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031361863

VL - 26

SP - 1585

EP - 1598

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 7

ER -