Renewed Looks at the Distribution of a Sum of Independent or Dependent Discrete Random Variables and Related Problems

Nitis Mukhopadhyay () and Sudeep R. Bapat ()
Additional contact information
Nitis Mukhopadhyay: University of Connecticut
Sudeep R. Bapat: University of California, Santa Barbara

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 3, 853-873

Abstract: Abstract Butler and Stephens (2017) have investigated the exact and approximate distributions of a sum S of independent binomial random variables with different probabilities. They used a convolution approach to find the exact distribution, whereas they heavily used the moments and cumulants to find approximations. We propose two different approaches. First, we show that the moment generating function (MGF) approach is easier and simpler to implement for finding the exact distribution of S. We also provide approximations for the distribution of S using large-scale computer simulations based on one million independent replications each. Such exact and approximate distributions are very close to analogous values reported in Butler and Stephens (2017). We show versatility of our approaches by including both exact and approximate distributions for the sum S of independent multinomial, geometric and other discrete random variables.

Keywords: Accuracies; Approximations; Dependent random variables; Exact calculations; Geometric distribution; Independent random variables; MGF approach; Moment generating function; Multinomial distributions; Poisson distribution; Simulation approach; 62E17; 62K10; 90B25 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-018-9690-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-018-9690-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-018-9690-8

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().