T[[S]]-NOETHERIAN PROPERTY ON GENERALIZED POWER SERIES MODULES

2019 ◽  
Vol 43 (1) ◽  
pp. 1-12
Author(s):  
Ahmad Faisol ◽  
Budi Surodjo ◽  
Sri Wahyuni
Keyword(s):  
Power Series ◽  
Generalized Power Series ◽  
Noetherian Property

On the Distribution of Sum of Independent Positive Binomial Variables

1970 ◽  
Vol 13 (1) ◽  
pp. 151-152 ◽  
Author(s):  
J. C. Ahuja
Keyword(s):  
Power Series ◽  
Inversion Formula ◽  
Probability Function ◽  
Random Variables ◽  
Random Variable ◽  
Characteristic Functions ◽  
Binomial Probability ◽  
Generalized Power Series ◽  
Alternative Derivation ◽  
Image Position

Let X1, X2, …, Xn be n independent and identically distributed random variables having the positive binomial probability function1where 0 < p < 1, and T = {1, 2, …, N}. Define their sum as Y=X1 + X2 + … +Xn. The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution.

Sign in / Sign up

Export Citation Format

Share Document