Determine Sample Size to Estimate the Average Parameter of a Heavy Tails Distribution Using Bayesian Methodology

Volume 9, Issue 3, June 2024     |     PP. 57-73      |     PDF (751 K)    |     Pub. Date: May 7, 2024
DOI: 10.54647/mathematics110484    30 Downloads     1898 Views  

Author(s)

Sarmad Abdulkhaleq Salih, University of Al-Hamdaniya , Mosul, Iraq
Omar Ramzi Jasim, University of Al-Hamdaniya , Mosul, Iraq.

Abstract
The generalized modified Bessel distribution is one of the most suitable mixed distributions. It is the result of mixing the normal distribution with the generalized inverse Gaussian distribution.
In this paper, The optimal sample size Analysis has been taken from the generalized modified Bessel population to estimate the mean parameter when the variance and shape parameters are known, using the informative prior information to estimate the mean parameter under the quadratic loss function. Then sampling and non-sampling approaches are used for the estimate of the parameter. Also, it has been noted that the posterior probability distribution for a mean parameter is following a generalized modified Bessel distribution. Through the simulation, we note Bayesian sample size is inversely proportional to the sampling cost (c) per unit.

Keywords
Generalized Modified Bessel Distribution, Quadratic Loss Function, Cost Function, Bayesian Sample Size.

Cite this paper
Sarmad Abdulkhaleq Salih, Omar Ramzi Jasim, Determine Sample Size to Estimate the Average Parameter of a Heavy Tails Distribution Using Bayesian Methodology , SCIREA Journal of Mathematics. Volume 9, Issue 3, June 2024 | PP. 57-73. 10.54647/mathematics110484

References

[ 1 ] Barndorff-Nielsen, O.,"Hyperbolic distributions and distributions on hyperbolae", Scand.J.Statist.5, P.P.151-157. 1978.
[ 2 ] Box, G.E.P. and Taio, G.C., “Bayesian inference in statistical Analysis”, Addition-Wesley Publishing Company, California, London, 1973.
[ 3 ] Butler, R. W., “Generalized inverse Gaussian distribution and their wishart connection", Colorado state university, Vol.25, P.P.69-75, USA, 1998.
[ 4 ] DeGroot, M.H., "Optimal statistical decision”, McGraw-Hill.1970.
[ 5 ] Hogg R. et al., "Introduction to Mathematical Statistics (6th edition)", Macmillan publishers company, New york, 2005.
[ 6 ] Hu, W., "Calibration of multivariate generalized hyperbolic distribution using the EM algorithm, With applications in risk management, Portfolio optimization and portfolio credit risk", Florida State University, Electronic theses, Treatises and Dissertation, The Graduate school, 2005.
[ 7 ] Koudou, A. E. and Ley, C., " Characterizations of GIG laws: a survey complemented with two new results", Proba. Surv. ,vol. 11 , p.p. 161-176, 2014.
[ 8 ] Lindley, D.V., "Bayesian statistics, a Review”, Philadelphia Society for Industrial and Applied Mathematics, 1972.
[ 9 ] Mora, J. A. N. & Mata, L. M., “Numerical aspects to estimate the generalized hyperbolic probability distribution”, Journal of Finance & Economics, vol. 1(4), p.p. 1-9, 2013.
[ 10 ] Press, S. J., "Subjective and objective Bayesian statistics”, A John Wiley and Sons, 2003.
[ 11 ] Saiful Islam, A. F. M., “Loss function, utility function and Bayesian sample size determination", PhD Thesis, University of London, 2011.
[ 12 ] Salih, S. A. and Aboudi, E. H., " Bayesian Inference of a Non-normal Multivariate Partial Linear Regression Model" Iraqi Journal of Statistical Science(34), pp. 91-115, 2021.
[ 13 ] Thabane, L. and Drekic, S., “Hypothesis testing for the generalized multivariate modified Bessel model", Journal of Multivariate Analysis,86, P.P.360-374, 2003.
[ 14 ] Thabane, L. & Haq, M. S., " The generalized multivariate modified Bessel distribution and its Bayesian applications", Journal of Applied Statistical Science, vol. 11(3), p.p.225-267, 2003.