TY - JOUR

T1 - Multivariate inverse trinomial distribution as a Lagrangian probability model

AU - Shimizu, Kunio

AU - Nishii, Nobuharu

AU - Minami, Mihoko

PY - 1997/1/1

Y1 - 1997/1/1

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.

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U2 - 10.1080/03610929708832002

DO - 10.1080/03610929708832002

M3 - Article

AN - SCOPUS:0031361863

SN - 0361-0926

VL - 26

SP - 1585

EP - 1598

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 7

ER -