Parameter Estimation and Hypothesis Testing on Bivariate Log Normal Regression Models
Kadek Budinirmala (a*), Purhadi (a), Achmad Choiruddin (a)

a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember,
Kampus ITS Sukolilo, Surabaya 60111, Indonesia
*budinirmala11[at]gmail.com

Abstract

The aims of this study is to introduce a bivariate Log-normal regression model and to develop technique for parameter estimation and hypothesis testing. We term the model Bivariate Log-Normal Regression (BLNR). The estimation procedure is conducted by the standard Maximum Likelihood Estimation (MLE) employing Newton-Raphson method. To perform hypothesis testing, we adapt the Maximum Likelihood Ratio Test (MLRT) for simultaneous testing with test statistics \(G^{2}\) which, for large n, follows Chi-square distribution with degrees of freedom p. In addition, the partial testing is derived from a central limit theorem which results in a Z-test statistic.

Keywords: BLNR- MLE- MLRT- Log-normal

Topic: Mathematics