ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
Manuscript Information
 
 
Improved Approximation Methods to the Stopped Sum Distribution
International Journal of Mathematical Analysis and Applications
Vol.4 , No. 6, Publication Date: Nov. 9, 2017, Page: 42-46
46 Views Since November 9, 2017, 16 Downloads Since Nov. 9, 2017
 
 
Authors
 
[1]    

Amani Al Rashidi, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[2]    

Bashair Al Juhani, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[3]    

Tahani Al Saeidi, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[4]    

Hanan Al Ahmadi, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[5]    

Mashael Al Harbi, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[6]    

Mawada Brri, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[7]    

Nada Al Johani, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

[8]    

Alya Almutairi, Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi Arabia.

 
Abstract
 

Most of the modern statistical models used the method that require the computation of probabilities from the complicated distribution such as (stopped sum) which can lead to intractable computation. However, in this study we will use a modern method to solve this problem, this method is called "Saddlepoint Approximation". However, In this study, we will derive the Saddlepoint Approximation (CDF) for some very complicated statistics such as stopped sum Geometric- Geometric distribution and stopped sum Negative binomial-bernoulli distribution.


Keywords
 

Approximations, Stopped Sum Distribution, Geometric, Negative Binomial-Bernoulli, Statistics, Probabilities


Reference
 
[01]    

Kuonen, Diego. "Computer-intensive statistical methods: saddlepoint approximations with applications in bootstrap and robust inference." PhD Thesis, Swiss Federal Institute of Technology (2001).

[02]    

Robin, Stéphane. "A compound Poisson model for word occurrences in DNA sequences." Journal of the Royal Statistical Society: Series C (Applied Statistics) 51.4 (2002): 437-451.

[03]    

Johnson, NL, Kotz, S.; Kemp, AW: Univariate discrete distributions. 2nd Ed. New York: John Wiley & Sons 1992.

[04]    

Johnson, Norman L., Adrienne W. Kemp, and Samuel Kotz. Univariate discrete distributions. Vol. 444. John Wiley & Sons, 2005.

[05]    

Minkova, Leda D. "The Pólya-Aeppli process and ruin problems." International Journal of Stochastic Analysis 2004.3 (1900): 221-234.

[06]    

Hogg, R. V., and A. T. Craig. "Introduction to Mathematical Statistics. Macmillan Publishing Company." NY, NY (1978).

[07]    

Al Mutairi Alya, O., and Heng Chin Low. "Saddlepoint Approximation to Cumulative Distribution Function for Poisson–Exponential Distribution." Modern Applied Science 7.3 (2013): 26.

[08]    

Al Mutairi, O., and Heng Chin Low. "Estimations of the Central Tendency Measures of the Random-sum Poisson-Weibull Distribution using Saddlepoint Approximation." Journal of Applied Sciences 14 (2014): 1889-1893.

[09]    

Shell, Richard. Handbook of industrial automation. CRC Press, 2000.

[10]    

Butler, Ronald W. Saddlepoint approximations with applications. Vol. 22. Cambridge University Press, 2007.





 
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