Journal of Statistical Research ISSN 0256 - 422 X 2008, Vol. 42, No. 2, pp. 99-104 Bangladesh EXTENDED CONFLUENT HYPERGEOMETRIC SERIES DISTRIBUTION AND SOME OF ITS PROPERTIES C. Satheesh Kumar Department of Statistics, University of Kerala, Trivandrum-695 581, India. Email: drcsatheeshkumar@gmail.com summary Here we introduce a new family of distributions namely the extended conflu- ent hypergeometric series (ECHS) distribution as a generalization of confluent hypergeometric series distributions, Crow and Bardwell family of distributions, displaced Poisson distributions and generalized Hermite distributions. Some im- portant aspects of the ECHS distributions such as probability mass function, mean, variance and recursion formulae for probabilities, moments and factorial moments are obtained. Keywords and phrases: Crow and Bardwell family of distributions; Displaced Poisson distribution; Hyper-Poisson distribution; Probability generating function AMS Classification: primary 60E05, 60E10; secondary 33C20 1 Introduction Hall (1956) has obtained some hypergeometric series distributions occurring in the study of birth and death processes and named it as the confluent hypergeometric series (CHS) distributions. Bhattacharya (1966) has discussed some of its properties and defined it as follows: A random variable X is said to have CHS distribution with parameters ν, λ and η if f (x)= P (X = x)= Γ(ν + x)Γ(λ) Γ(λ + x)Γ(ν ) × η x 1 F 1 (ν ; λ; η) , (1.1) where ν> 0, λ> 0, η> 0; x =0, 1, 2,... and 1 F 1 (ν ; λ; η) is the confluent hypergeometric function (for details see Mathai and Saxena, 1973 or Slater, 1960). Several well-known discrete distributions such as Poisson distribution, displaced Poisson distribution of Staff (1964) and Hyper-Poisson distribution of Bardwell and Crow (1964) are special cases of the CHS distribution. Inference for this family has been attempted by Gurland and Tripathi (1975) and Tripathi and Gurland (1977, 1979). The probability generating function (p.g.f.) of the CHS distribution is the following, in which δ =[ 1 F 1 (ν ; λ; η)] -1 . H (z )= δ 1 F 1 (ν ; λ; ηz ) (1.2) c  Institute of Statistical Research and Training (ISRT), University of Dhaka, Dhaka 1000, Bangladesh.