doi: **10.7392/openaccess.70081979**

**Mundia S.M. **[1], **Gichuhi A.W. **[2], **Kihoro J.M. **[2]

[1] Department of Actuarial & Statistics, DeKUT; [2] Department of Actuarial & Statistics, JKUAT

Statistically, change point is the location or the time point such that observations follow one distribution up to the point and then another afterwards. Change point problems are encountered in our daily life and in disciplines such as economics, ﬁnance, medicine, geology, Literature among others. In this paper, the power of the likelihood ratio tests for a change point in binomial observations whose mean is dependent on the explanatory variables was investigated. Artiﬁcial neural network technique was used to estimate the conditional means. It was shown through simulation that the power of the test increases as the size of sample. The test was found to have less power when the change point was near the edges than when the change point is at the centre. The test was more likely to detect a change if the magnitude of the change was large.

**Keywords: ** change point, likelihood ratio test, binomial distribution, power of a test, artiﬁcial neural-network.

**Citation: **Maina, M. S., Gichuhi, W. A., & Mwaniniki, K. J. (2013). The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution. *Open Science Repository Mathematics*, Online(open-access), e70081979. doi:10.7392/openaccess.70081979

**Received:** June 23, 2013

**Published: **June 27, 2013

**Copyright:** © 2013 Maina, M. S., Gichuhi, W. A., & Mwaniniki, K. J. Creative Commons Attribution 3.0 Unported License.

**Contact:** research@open-science-repository.com

Other download options: cloud 2; cloud 3.

**APA**

Maina, M. S., Gichuhi, W. A., & Mwaniniki, K. J. (2013). The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution. *Open Science Repository Mathematics*, Online(open-access), e70081979. doi:10.7392/openaccess.70081979

**MLA**

Maina, Mundia Simon, Waititu Anthony Gichuhi, and Kihoro John Mwaniniki. “The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution.” *Open Science Repository Mathematics* Online.open-access (2013): e70081979.

**Chicago**

Maina, Mundia Simon, Waititu Anthony Gichuhi, and Kihoro John Mwaniniki. 2013. “The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution.” *Open Science Repository Mathematics* Online (open-access): e70081979. doi:10.7392/openaccess.70081979. http://www.open-science-repository.com/mathematics-70081979.html.

**Harvard**

Maina, M.S., Gichuhi, W.A. & Mwaniniki, K.J., 2013. The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution. *Open Science Repository Mathematics*, Online(open-access), p.e70081979. Available at: http://www.open-science-repository.com/mathematics-70081979.html.

**Science**

1. M. S. Maina, W. A. Gichuhi, K. J. Mwaniniki, The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution, *Open Science Repository Mathematics* **Online**, e70081979 (2013).

**Nature**

1. Maina, M. S., Gichuhi, W. A. & Mwaniniki, K. J. The Power of Likelihood Ratio Test for a Change Point in Binomial Distribution. *Open Science Repository Mathematics* **Online**, e70081979 (2013).

Research registered in the DOI resolution system as:** ****10.7392/openaccess.70081979**.

**Instructions**

Main criteria reviewers should evaluate are: originality, sound methodology and data, following of universal ethical principles, scientific relevance and clear description of problems, hypotheses and results.

Names, affiliations of reviewers and personal contacts should be included at the end of the text.

Maximum text length is 10000 characters. **Only serious, consistent and original reviews are accepted.**

This work is licensed under a Creative Commons Attribution 3.0 Unported License.