Lindely’s method to estimate the parameters of the univariate truncated t Regression Model using informative prior information

Abstract

   In this paper, the parameters of the truncated t-regression model were estimated, in which the response variable follows a two-sided truncated t-distribution, and its parameters were estimated by an approximate Bayesian technique according to Lindley's method. Parameters were estimated when ?² and ? were unknown when the truncated t regression simple linear model was univariate. Informative prior information are used to estimate the parameters of the univariate model when the truncating points and the degree of freedom are known and with different cases of them .

 On the application side, experimental samples were generated by using the inverse function method. The application was carried out by relying on the Matlab program (14b) and according to different sample sizes, which are 10, 20 and 30 with degrees of freedom 3 and 6, truncated points were selected from two sides ranging within the following periods:  ( -3 , + 3 ) , ( -2 , + 2 ), ( -1 , + 1) , as well as for one term only, once from the left side for intervals (-3,0), (-2,0), (- 1.0) and the other from the right side for the periods (0, +3), (0, +2), (0, +1), and the risk function was relied on in measuring the preference in relation to the sample size or the degree of freedom. It was concluded that the inverse relationship between the risk function on the one hand and the sample size and degrees of freedom on the other hand, as the increase in the sample size leads to a decrease in the risk function and also the greater the degree of freedom the more this leads to a decrease in the risk function.

It was also concluded that the breadth of the truncated area leads to a decrease in the value of the risk function.