TY - JOUR

T1 - Minimum Variance Unbiased Estimation for the Lagrange Power Series Distributions

AU - Consul, P. C.

AU - Famoye, F.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - It is shown that the modified power series distribution (MPSD) [Gupta, 1974], the Lagrange probability distribution (LPD) [Consul and Shenton, 1972], the Lagrange power series distribution (LPSD) [Jain, 1975] and the discrete exponential family (DEF) distribution [Janardan, 1982) represent the same probability model. A theorem on the MVU estimation of a function 1(0) of the parameter 6 in the LPSD is stated with the nccessary conditions. The theorem is then applied to derive the MVU estimators for the mean, square of the mean and the variance of the generalized Poisson distribution, generalized negative binomial distribution and some other related distributions.

AB - It is shown that the modified power series distribution (MPSD) [Gupta, 1974], the Lagrange probability distribution (LPD) [Consul and Shenton, 1972], the Lagrange power series distribution (LPSD) [Jain, 1975] and the discrete exponential family (DEF) distribution [Janardan, 1982) represent the same probability model. A theorem on the MVU estimation of a function 1(0) of the parameter 6 in the LPSD is stated with the nccessary conditions. The theorem is then applied to derive the MVU estimators for the mean, square of the mean and the variance of the generalized Poisson distribution, generalized negative binomial distribution and some other related distributions.

KW - Lagrange power series distributions

KW - MVU estimable

KW - Minimum variance unbiased estimator

UR - http://www.scopus.com/inward/record.url?scp=84972996262&partnerID=8YFLogxK

U2 - 10.1080/02331888908802188

DO - 10.1080/02331888908802188

M3 - Article

AN - SCOPUS:84972996262

VL - 20

SP - 407

EP - 415

JO - Statistics

JF - Statistics

SN - 0233-1888

IS - 3

ER -