A tutorial on how to efficiently calculate and format tables of the binomial distribution
Other Title(s)
شرح تعليمي عن كيف تحسب و تشكل بكفاءة جداول التوزيع ذي الحدين
Joint Authors
al-Qasimi, Abd al-Ghani Muhammad
Rushdi, Ali Muhammad Ali
Source
Journal of King Abdulaziz University : Engineering Sciences
Issue
Vol. 19, Issue 1 (30 Jun. 2008), pp.3-17, 15 p.
Publisher
King Abdulaziz University Scientific Publishing Center
Publication Date
2008-06-30
Country of Publication
Saudi Arabia
No. of Pages
15
Main Subjects
Abstract EN
Owing to the importance of the binomial distribution, tables for its probability mass function (PMF) and its cumulative distribution function (CDF) have been extensively published.
This paper presents a tutorial on a novel technique for constructing and recording these tables.
The tables are to be compiled with a high precision and a minimal round-off error through the use of highly efficient iterative algorithms based on binary recursive relations for the PMF and the CDF.
The computational cost for each additional table entry is merely a single multiplication plus two additions.
This remarkably low cost is due to the fact that each entry is computed in terms of exactly two preceding entries.
Certain symmetries and limiting values are noted, thereby allowing a considerable reduction in the number of listed entries.
Table entries are given in compact forms of fixed-point or floating-point format, with an objective of minimizing the numerical uncertainty that arises when representing an entry in a limited field width, i.e., when using a limited number of digit or character positions.
This kind of novel format is crucial for accurate evaluation of probabilities associated with ultra-high reliability systems or with very rare events.
American Psychological Association (APA)
al-Qasimi, Abd al-Ghani Muhammad& Rushdi, Ali Muhammad Ali. 2008. A tutorial on how to efficiently calculate and format tables of the binomial distribution. Journal of King Abdulaziz University : Engineering Sciences،Vol. 19, no. 1, pp.3-17.
https://search.emarefa.net/detail/BIM-329933
Modern Language Association (MLA)
al-Qasimi, Abd al-Ghani Muhammad& Rushdi, Ali Muhammad Ali. A tutorial on how to efficiently calculate and format tables of the binomial distribution. Journal of King Abdulaziz University : Engineering Sciences Vol. 19, no. 1 (2008), pp.3-17.
https://search.emarefa.net/detail/BIM-329933
American Medical Association (AMA)
al-Qasimi, Abd al-Ghani Muhammad& Rushdi, Ali Muhammad Ali. A tutorial on how to efficiently calculate and format tables of the binomial distribution. Journal of King Abdulaziz University : Engineering Sciences. 2008. Vol. 19, no. 1, pp.3-17.
https://search.emarefa.net/detail/BIM-329933
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 16
Record ID
BIM-329933