Authors :
M.A ADIO; O.U. ODUKOYA
Volume/Issue :
Volume 7 - 2022, Issue 3 - March
Google Scholar :
https://bit.ly/3IIfn9N
Scribd :
https://bit.ly/3LbbGeV
DOI :
https://doi.org/10.5281/zenodo.6471750
Abstract :
The Gross Domestic Product (GDP) measures
all commodities and services generated in the country,
regardless of whether they are produced by domestic or
foreign firms. It examines the country's economic
growth, pattern, and rate. As a result, the focus of this
research is on Nigeria's GDP rate.
The data was subjected to exploratory data analysis
(GDP rate).The data's minimum and maximum values
were established. Easy fit was used to match the optimal
distribution for the data set after the histogram and box
plot were shown. In order to determine their respective
posterior distributions, the Bayes theorem was also
applied to both the conjugate and non-informative
priors.
The two priors' posterior means and standard
deviations, as well as their credible intervals, were
calculated.The results showed that the mean and
standard deviation for the data were 1411.6 and
928.8775, with the minimum and maximum values to be
383 and 3567 respectively. The histogram showed that
the data is positively skewed to the right, the box plot
indicated the lower and the upper quartiles were 620 and
2187. The application of Bayes theorem to the data set,
assumed a beta distribution for conjugate prior, while a
uniform distribution was assumed for the Noninformative prior. The parameter values for the
conjugate prior, the likelihood and the posterior
distributions were Beta(4.21,7.39), Beta(5.07,10.83) and
Beta(8.28 and 17.01) respectively. The posterior Mean
(Bayes estimate) and Standard deviation as well as 95%
credible interval for Beta prior were 0.32373, 0.0917 and
[0.31, 0.34]. Also the Posterior mean, standard deviation
as well as the 95% credible interval for the uniform prior
were 0.3229, 0.114543 and [0.20836, 0.4374].
The posterior mean for the uniform prior was
higher than the posterior mean for the conjugate prior,
the credible interval for the conjugate prior was closer
than the credible interval for the uniform prior, and the
posterior standard deviation for the conjugate prior was
higher than the posterior standard deviation for the
uniform prior.
As a result, the conjugate prior outperforms the
uniform prior. Beta likelihood is recommended for
fitting the rate of GDP in Nigeria.
Keywords :
Beta distribution, Uniform Prior, Credible Interval, Bayes estimates, Posterior distribution.
The Gross Domestic Product (GDP) measures
all commodities and services generated in the country,
regardless of whether they are produced by domestic or
foreign firms. It examines the country's economic
growth, pattern, and rate. As a result, the focus of this
research is on Nigeria's GDP rate.
The data was subjected to exploratory data analysis
(GDP rate).The data's minimum and maximum values
were established. Easy fit was used to match the optimal
distribution for the data set after the histogram and box
plot were shown. In order to determine their respective
posterior distributions, the Bayes theorem was also
applied to both the conjugate and non-informative
priors.
The two priors' posterior means and standard
deviations, as well as their credible intervals, were
calculated.The results showed that the mean and
standard deviation for the data were 1411.6 and
928.8775, with the minimum and maximum values to be
383 and 3567 respectively. The histogram showed that
the data is positively skewed to the right, the box plot
indicated the lower and the upper quartiles were 620 and
2187. The application of Bayes theorem to the data set,
assumed a beta distribution for conjugate prior, while a
uniform distribution was assumed for the Noninformative prior. The parameter values for the
conjugate prior, the likelihood and the posterior
distributions were Beta(4.21,7.39), Beta(5.07,10.83) and
Beta(8.28 and 17.01) respectively. The posterior Mean
(Bayes estimate) and Standard deviation as well as 95%
credible interval for Beta prior were 0.32373, 0.0917 and
[0.31, 0.34]. Also the Posterior mean, standard deviation
as well as the 95% credible interval for the uniform prior
were 0.3229, 0.114543 and [0.20836, 0.4374].
The posterior mean for the uniform prior was
higher than the posterior mean for the conjugate prior,
the credible interval for the conjugate prior was closer
than the credible interval for the uniform prior, and the
posterior standard deviation for the conjugate prior was
higher than the posterior standard deviation for the
uniform prior.
As a result, the conjugate prior outperforms the
uniform prior. Beta likelihood is recommended for
fitting the rate of GDP in Nigeria.
Keywords :
Beta distribution, Uniform Prior, Credible Interval, Bayes estimates, Posterior distribution.
