EconPapers    
Economics at your fingertips  
 

On the number of trials needed to obtain k consecutive successes

Steve Drekic and Michael Z. Spivey

Statistics & Probability Letters, 2021, vol. 176, issue C

Abstract: A sequence of independent Bernoulli trials, each of which is a success with probability p, is conducted. For k∈Z+, let Xk be the number of trials required to obtain k consecutive successes. Using techniques from elementary probability theory, we present a derivation which ultimately yields an elegant expression for the probability mass function of Xk, and is simpler in comparison to what is found in the literature. Following this, we use our derived formula to obtain explicit closed-form expressions for the complementary cumulative distribution function and the nth factorial moment of Xk.

Keywords: Bernoulli trials; Consecutive successes; Factorial moments; Generating function; Polynomial coefficients; Bell polynomials (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221000948
Full text for ScienceDirect subscribers only

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:eee:stapro:v:176:y:2021:i:c:s0167715221000948

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2021.109132

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2021-06-30
Handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221000948