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THE POWER OF THE PARAMETER HYPOTHESIS ON PARETO AND BETA DISTRIBUTIONS
Keywords:
power of the hypothesis, Pareto distribution, beta distribution, R‑code.DOI:
https://doi.org/10.17654/0972087123004Abstract
The paper discusses the power and size of the hypothesis testing of the parameter shape on the Pareto and beta distributions. We determine and graphically analyze the power and size on both two continuous (Pareto and beta) distributions. Indeed, the work is devoted to derive the formula of the power for both distributions. The four steps to derive the power and size functions are as follow: (1) determine the sufficiently statistics, (2) compute the rejection area, (3) derive the formula of the power, and (4) determine the graphs using generated (simulation) data. Due to the complicated formula of the power, we then computed and plotted the curves using R-code. The graphic analyze is then given. The results showed that the power and size of the Pareto distribution decrease as the critical value for the rejection area (k) increases. Here, we noted that the scale parameter (p) also significantly affected the curves of the power. The size is constant and similar on different p’s. In the context of beta distribution, the power and size really depended on the rejection area (k) and parameter shape (b). The maximum power occurs for small k, and the minimum size occurs for large k.
Received: November 5, 2022
Accepted: January 2, 2023
References
A. K. Md. E. Saleh, Theory of Preliminary Test and Stein-type Estimation with Applications, John Wiley and Sons, Inc., New Jersey, 2006.
B. Pratikno, Test of hypothesis for linear models with non-sample prior information, Unpublished Ph.D. Thesis, University of Southern Queensland, Australia, 2012.
B. Pratikno, The noncentral t distribution and its application on the power of the tests, Far East J. Math. Sci. (FJMS) 106(2) (2018), 463-474.
B. Pratikno, G. M. Pratidina and Setianingsih, Power of hypothesis testing parameters shape of the distributions, Far East J. Math. Sci. (FJMS) 110(1) (2019), 15-22.
D. D. Wackerly, W. Mendenhall III and R. L. Scheaffer, Mathematical Statistics with Application, 7th ed., Thomson Learning, Inc., Belmont, CA, USA, 2008.
R. M. Yunus, Increasing power of M-test through pre-testing, Unpublished Ph.D. Thesis, University of Southern Queensland, Australia, 2010.
R. M. Yunus and S. Khan, Test for intercept after pre-testing on slope a robust method, 9th Islamic Countries Conference on Statistical Sciences (ICCS-IX): Statistics in the Contemporary World - Theories, Methods and Applications, 2007.
R. M. Yunus and S. Khan, Increasing power of the test through pre-test a robust method, Comm. Statist. Theory Methods 40 (2011a), 581-597.
R. M. Yunus and S. Khan, M-tests for multivariate regression model, J. Nonparametr. Stat. 23 (2011b), 201-218.
R. M. Yunus and S. Khan, The bivariate noncentral chi-square distribution - a compound distribution approach, Appl. Math. Comput. 217 (2011c), 6237-6247.
R. Walpole, R. H. Myers, S. L. Myers and K. Ye, Probability and Statistics for Engineers and Scientists, Pearson, Inc, USA, 2012.
S. Khan, B. Pratikno, A. I. N. Ibrahim and R. M. Yunus, The correlated bivariate non-central F distribution and its application, Comm. Statist. Simulation Comput. 45 (2016), 3491-3507.
S. Khan, Estimation of the parameters of two parallel regression lines under uncertain prior information, Biom. J. 44 (2003), 73-90.
S. Khan, Estimation of parameters of the multivariate regression model with uncertain prior information and Student-t errors, J. Statist. Res. 39(2) (2005), 79-94.
S. Khan, Shrinkage estimators of intercept parameters of two simple regression models with suspected equal slopes, Comm. Statist. Theory Methods 37 (2008), 247-260.
S. Khan and A. K. Md. E. Saleh, Preliminary test estimators of the mean based on p-samples from multivariate Student-t populations, Bulletin of the International Statistical Institute, 50th Session of ISI, Beijing, 1995, pp. 599-600.
S. Khan and A. K. Md. E. Saleh, Shrinkage pre-test estimator of the intercept parameter for a regression model with multivariate Student-t errors, Biom. J. 39 (1997), 1-17.
S. Khan and A. K. Md. E. Saleh, On the comparison of the pre-test and shrinkage estimators for the univariate normal mean, Statist. Papers 42(4) (2001), 451-473.
S. Khan, Z. Hoque and A. K. Md. E. Saleh, Improved estimation of the slope parameter for linear regression model with normal errors and uncertain prior information, J. Statist. Res. 31(1) (2002), 51-72.
S. Khan and Z. Hoque, Preliminary test estimators for the multivariate normal mean based on the modified W, LR and LM tests, J. Statist. Res. 37 (2003), 43-55.
S. Khan and A. K. Md. E. Saleh, Estimation of intercept parameter for linear regression with uncertain non-sample prior information, Statist. Papers 46 (2005), 379-394.
S. Khan and A. K. Md. E. Saleh, Estimation of slope for linear regression model with uncertain prior information and Student-t error, Comm. Statist. Theory Methods 37(16) (2008), 2564-258.
S. Khan and B. Pratikno, Testing base load with non-sample prior information on process load, Statist. Papers 54(3) (2013), 605-617.
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