BAYESIAN APPROXIMATIONS FOR SHAPEPARAMETER OF GENERALIZED POWER FUNCTION DISTRIBUTION
Keywords:
Bayesian Estimation, Prior Distribution, Normal Approximation, Lindley’s Approximation, Laplace Approximation.Abstract
Power function distribution provides a better fit for failure data and more appropriate information about reliability and hazard rates and used as a subjective description of a population for which there is limited sample data and in case where the relationship between variables is known but data is scare. In this paper, Bayesian approximation techniques like normal approximation, Lindley’s Approximation, Laplace Approximation are used to study the behavior of shape parameter of generalized power function distribution under different priors. Furthermore, a comparison of these approximation techniques, under different priors is studied by making use of simulation technique.
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Ahmad, S.P, Ahmad, A. and Khan, A.A. (2011). Bayesian analysis of gamma
distribution using SPLUS and R-software, Asian Journal of Mathematics and
Statistics, Vol. 4(4), p. 224-233.
Ahmed, A.A., Khan. A. A., and Ahmed, S.P. (2007). Bayesian analysis of
exponential distribution in S-PLUS and R Softwares, Sri Lankan Journal of
Applied Statistics, Vol. 8, p. 95-109.
Almutairi, A. O. and Heng, C. L. (2012). Bayesian estimate for shape
parameter from generalized power function distribution, Mathematical Theory
and Modelling, 2, p. 2224-5804.
Balakrishnan, N. and Chan, P. (1994). Asymptotic best linear unbiased
estimation for the log-Gamma distribution, Sankhya, Vol. 56, p. 314-322.
Balakrishnan, N. and Mi, J. (2003). Existence and uniqueness of the MLE for
normal distribution based on general progressively Type-II censored samples,
J. Statistics & Probability Letters, 64, p. 407-414.
Berger, J. O. and Wolpert, R. (1984). The Likelihood Principle. Harvard,
California: Institute Of Mathematical Statistics.
Chang, S.K. (2007). Characterizations of the power function distribution by
the independence of record values, Journal of the Chung Cheong
Mathematical Society, 20 (2), p. 139-146.
Freedman, L. S., Spiegel halter, D. J. and Parmar, M. K. V. (1994). The what,
why, and how of Bayesian clinical trials monitoring, Statistics in Medicine,
, p. 1371-1383
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995). Bayesian Data
Analysis, Chapman and Hall, London.
Khan, A. A., Puri, P. D. and Yaquab, M. (1996). Approximate Bayesian
inference in location–scale models. Proceedings of national seminar on
Bayesian Statistics and Applications, April 6-8, p. 89-101, Deptt. of Statistics
BHU, Varanasi, India.
Kifayat, T., Aslam, M and Ali, S. (2012). Bayesian inference for the parameter
of the power distribution, Journal of Reliability and Statistical Studies, 5(2), p.
-58.
Lindley, D. V. (1958). Fiducial distributions and Bayes theorem, Journal of the
Royal Statistical Society, B, 20, p. 102-107.
Meniconi, M. and Barry, D.M. (1996). The Power function distribution:
auseful and simple distribution to assess electrical component reliability,
Microelectronics Reliability, 36 (9), p. 1207-1212.
Pandey, H. and Rao, A. K. (2008). Bayesian estimation of the shape parameter
of a generalized Pareto distribution under asymmetric loss functions,
Hacettepe Journal of Mathematics and Statistics, Vol, 83, p. 69-83.
Pratt, J. W. (1965). Bayesian interpretation of standard inference statements
(with discussion), Journal of the Royal Statistical Society, B 27, p. 169-203.
Rahman, H., Roy, M. K.and Baizid, A. K. (2012). Bayes Estimation under
conjugate Prior for the case of power function distribution, American Journal
of Mathematics and Statistics, 2(3), p. 44-48.
Rubin, D.B. and Schenker, N. (1987). Logit-based interval estimation for
binomial data using the Jeffrey’s prior, Sociological Methodologies, Vol, 17,
p. 131-144.
Saran, J. and Pandey, A. (2004). Estimation of parameters of a power function
distribution and its characterization by kth record values, Journal Statistica, 14
(3), p. 523-536.
Sultan, R., Sultan, H.and Ahmad, S.P. (2014). Bayesian analysis of power
function distribution under double priors, Journal of Statistics Applications
and Probability, 3(2), p. 1-6.
Tierney. L. and Kadane. J. (1986). Accurate approximations for posterior
moments and marginal densities, Journal of the American Statistical
Association, 81, p. 82-86.
