Bayesian Transmuted Normal Distribution With β and σ Parameters Where X' s Are Correlated

Abstract

Transmuted distribution emerged as new form of distribution in the literature recently, this is due to influx and changing nature of data from the conventional structured to semi and unstructured data. The study developed new distribution in practical term by incorporating regression variables into normal distribution and direct Bayesian gradient Monte Carlo simulation (DBGMS). The data were subjected to multicollinearity in a low dimension with specified 𝜌 and transmuted parameter 𝜆 were specified as 0.3, 0.6 and 0.9. The outcome of the study pointed to the fact that Bayes estimate and posterior mean of DBGMS is superior and more efficient to classical maximum likelihood estimates. The study therefore recommended DBGMS when data are multicollinear and transmuted distribution is in use.