THE LINDSAY TRANSFORM OF NATURAL EXPONENTIAL-FAMILIES

被引:9
作者
KOKONENDJI, CC
SESHADRI, V
机构
[1] UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
[2] MCGILL UNIV,MONTREAL H3A 2T5,QUEBEC,CANADA
来源
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE | 1994年 / 22卷 / 02期
关键词
CONVOLUTION; CUBIC VARIANCE; EXPONENTIAL FAMILIES; INFINITELY DIVISIBLE MEASURES; LEVY MEASURES; NATURAL EXPONENTIAL FAMILIES; VARIANCE FUNCTIONS;
D O I
10.2307/3315588
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Let mu be an infinitely divisible positive measure on R. If the measure rho(mu) is such that x-2[rho(mu(dx)-rho(mu({0})delta0(dx)] is the Levy measure associated with mu and is infinitely divisible, we consider for all positive reals alpha and beta the measure T(alpha,beta)(mu) which is the convolution of mu(alpha) and rho(mu)beta. For example, if mu is the inverse Gaussian law, then rho(mu) is a gamma law with parameter 3/2. Then T(alpha,beta)(mu) is an extension of the Lindsay transform of the first order, restricted to the distributions which are infinitely divisible. The main aim of this paper is to point out that it is possible to apply this transformation to all natural exponential families (NEF) with strictly cubic variance functions P. We then obtain NEF with variance functions of the form square-root DELTAP(square-root DELTA), where DELTA is an affine function of the mean of the NEF. Some of these latter types appear scattered in the literature.
引用
收藏
页码:259 / 272
页数:14
相关论文
共 18 条
[1]   STATISTICAL-INFERENCE FOR A CLASS OF MODIFIED POWER-SERIES DISTRIBUTION WITH APPLICATIONS TO RANDOM MAPPING-THEORY [J].
BERG, S ;
NOWICKI, K .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1991, 28 (02) :247-261
[2]   RANDOM MAPPINGS WITH AN ATTRACTING CENTER - LAGRANGIAN DISTRIBUTIONS AND A REGRESSION FUNCTION [J].
BERG, S ;
MUTAFCHIEV, L .
JOURNAL OF APPLIED PROBABILITY, 1990, 27 (03) :622-636
[3]  
BERG S, 1992, RANDOM GRAPHS, V2, P1
[4]  
DIEUDONNE J, 1971, INFINITESIMAL CALCUL
[5]   LAGRANGE DISTRIBUTIONS OF THE 2ND KIND AND WEIGHTED DISTRIBUTIONS [J].
JANARDAN, KG ;
RAO, BR .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1983, 43 (02) :302-313
[6]  
JORGENSEN B, 1987, J ROY STAT SOC B MET, V49, P127
[7]  
KOKONENDJI CC, 1992, CR ACAD SCI I-MATH, V314, P1063
[8]   NATURAL REAL EXPONENTIAL-FAMILIES WITH CUBIC VARIANCE FUNCTIONS [J].
LETAC, G ;
MORA, M .
ANNALS OF STATISTICS, 1990, 18 (01) :1-37
[9]  
LETAC G, 1991, 48TH P SESS INT STAT, V54, P1
[10]  
LETAC G, 1987, J ROY STAT SOC B MET, V49, P154