Bayesian Transmuted Normal Distribution With β and σ Parameters Where X' s Are Correlated
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Date
2024
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Publisher
Journal of Probability and Statistical Science
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.
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Keywords
Bayesian, transmuted, gradient, multicollinearity, Gibbs