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Vol.4 , No. 6, Publication Date: Nov. 9, 2017, Page: 42-46
 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.&picture=http://www.aascit.org/aascit/decorators/img/journal/921.jpg)
| [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. |
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
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| [04] | Johnson, Norman L., Adrienne W. Kemp, and Samuel Kotz. Univariate discrete distributions. Vol. 444. John Wiley & Sons, 2005. |
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| [06] | Hogg, R. V., and A. T. Craig. "Introduction to Mathematical Statistics. Macmillan Publishing Company." NY, NY (1978). |
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| [09] | Shell, Richard. Handbook of industrial automation. CRC Press, 2000. |
| [10] | Butler, Ronald W. Saddlepoint approximations with applications. Vol. 22. Cambridge University Press, 2007. |
