### Journals Information

**
Mathematics and Statistics Vol. 10(4), pp. 844 - 850 DOI: 10.13189/ms.2022.100415 Reprint (PDF) (454Kb) **

## The Power and Its Graph Simulations on Discrete and Continuous Distributions

**Budi Pratikno ^{*}, Nailatul Azizah , Avita Nur Azizah **

Department of Mathematics, Faculty of Mathematics and Natural Science, Jenderal Soedirman University, Purwokerto, Indonesia

**ABSTRACT**

We determined the power and its graph simulations on the discrete Poisson and Chi-square distributions. There are four important steps of the research methodology summarized as follow: (1) determine the sufficient statistics (if possible), (2) create the rejection area (UMPT test is sometime used), (3) derive the formula of the power, and (4) determine the graphs using the data (in simulation). The formula of the power and their curves are then created using code. The result showed that the power of the illustration of the discrete (Binomial distribution) depended on the number of trials and bound of the rejection area. The curve of the power is sigmoid (-curve) and tends to be zero when parameter shape () is greater than 0.4. It decreases (started from = 0.2) as the parameter theta increases. In the Poisson context, the curve of the power of the Poisson distribution is not -curve, and it only depends on the parameter shape . We note that the curve of the power of the Poisson is quickly to be one for greater than 2 and less than 10. In this case, the size of the Poisson distribution is greater than 0.05, so it is not a reasonable thing even the power is close to be one. In this context, we have to choose the maximum power and minimum size. In the context of Chi-square distribution, the graph of the power and size functions depend on rejection region boundary (). Here, we note that skewness of the -curve is positive as the increases. Similarly, the size also depends on the (and constant), and it decrease as the increases. We here also noted that the power is quickly to be one for large degree of freedom ().

**KEYWORDS**

Poisson Discrete Distribution, Chi-Square Continuous Distribution, Parameter Shape, R-code

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Budi Pratikno , Nailatul Azizah , Avita Nur Azizah , "The Power and Its Graph Simulations on Discrete and Continuous Distributions," Mathematics and Statistics, Vol. 10, No. 4, pp. 844 - 850, 2022. DOI: 10.13189/ms.2022.100415.

(b). APA Format:

Budi Pratikno , Nailatul Azizah , Avita Nur Azizah (2022). The Power and Its Graph Simulations on Discrete and Continuous Distributions. Mathematics and Statistics, 10(4), 844 - 850. DOI: 10.13189/ms.2022.100415.