Track: Statistics

Abstract

The research studied  the power on specified continuous distributions, namely  Lognormal and Logistics  distributions. Here, we derived the formula of the power of the Lognormal and Logistics  distributions at least in two steps: (1) create sufficient statistic and rejection region for getting the bound of the area, and (2) derived the formula using the bound of the rejection area or using the basic concept of the definition of the power. To get the power and size, we here must define the hypothesis testing of the parameter shape in term of one-side hypothesis testing. This is due to the parameter shape are greater than zero. The Graphically analysed is given to make an easier interpretation, so a simulation is then given to figure their curve. R code is then used to compute and plot the curves. The result showed that Lognormal distribution depended on the degree of freedom n, bound of the rejection area and parameter shape (sigma ).  Moreover, we also noted that the curves of the power are sigmoid and they increase (more) faster (going to be one) on the small parameter shape (sigma ) and large n. The size is constant and remain unchanged, and here the eligible size is 0.049 close to level of significance 0.05. So, we accepted this size as the minimum size (close to 0.05). In the context of the Logistics distribution, the result showed that the power of the Logistics distribution increase as the k increases, and the highestt curve occurs on large k (k=10), but not for  the  sigma . Generally, the size is constant and it does not significantly change the curve on several k.  Moreover, the size increase as the k increases. We noted here that the highest size occurs on k=10, and its value is around 1.0. This size is an impossible thing (not reasonable) to be used (far way from 0.05). However, we must choose the small size (less than 0.05), so we did not recommend this size. In this research, our target is to choose the maximum power and minimum size.