Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location

Statistical Inference of Normal Distribution Based on Several Divergence Measures: A Comparative Study

“…(5) From the results of part (3) above and using Equation ( 5) we obtain the r-order-and-sdegree divergence measure and its average under the prior distribution of θ 1 between g(v|θ 1 ) and h(v|w ) as required. (6) Substituting r = 2 in the relative-information-of-type-r measure found in part (4) above, we obtain the chi-square divergence and its average under the prior distribution of θ 1 between g(v|θ 1 ) and h(v|w ) as required. Note that Aχ 2 (g∥h…”

“…( 5) From the results of part (3) above, and using Equation ( 5), we obtain the r-order-ands-degree divergence measure and its average under the distribution of W between g(v; θ 1 ) and q(v|w ) as required. ( 6) Substituting r = 2 in the relative-information-of-type-r measure found in part (4) above, we obtain the chi-square divergence and its average under the distribution of W between g(v; θ 1 ) and q(v|w ) as required. ( 7) Substituting r = 1 2 in the relative-information-of-type-r measure found in part (4) above and then multiplying by 1 2 , we obtain the Hellinger measure and its average under the distribution of W between g(v; θ 1 ) and q(v|w ) as required.…”

“…One of the many possible forms of prediction is the Bayesian predictive approach, which was first introduced by Aitchison [1], who demonstrated its advantage on the Kullback-Leibler (KL) divergence over plug-in predictive densities. Bayesian predictive-density estimation has been applied to different statistical models, including but not limited to the following: Aitchison and Dunsmore [2], who obtained Bayesian predictive distributions based on random samples from binomial, Poisson, gamma, twoparameter exponential, and normal distributions; Escobar et al [3], who discussed the application of Bayesian inference to density-estimation models, using Dirichlet-process mixtures; and Hamura et al [4], who used a number of Bayesian predictive densities to introduce prediction for the exponential distribution. Hamura et al [5] studied the Bayesian prediction distribution of a chi-squared distribution, given a random sample from another chi-squared distribution under the Kullback-Leibler divergence.…”

Bayesian Point Estimation and Predictive Density Estimation for the Binomial Distribution with a Restricted Probability Parameter

“…Fourdrinier et al (2011), Hamura and Kubokawa (2019), and Hamura and Kubokawa (2020) treated the normal, negative binomial, and Poisson cases by using identies which relate Bayesian predictive density estimation to Bayesian point estimation. L'Moudden et al (2017) and Hamura and Kubokawa (2021) considered the gamma and exponential cases directly. General results for location and/or scale families were obtained by Kubokawa et al (2013).…”