A recently proposed asymmetric loss function, termed the exponential squared error loss function, has been applied to estimation problems. However, prediction methodologies based on this loss function remain unexplored in the literature. In this paper, we focus on Bayesian two-sample prediction for the exponential distribution under this new loss function. We consider situations where the informative sample size may be either fixed or random. Since the Bayesian predictors do not have closed forms, we employ a Monte Carlo method to approximate them. A simulation study is conducted to evaluate the performance of the predictors. The simulation results indicate that predictors with fixed sample sizes can outperform those with truncated Poisson and truncated geometrically distributed sample sizes. A real data example is also presented for illustration. The paper concludes with a discussion.

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property was and is well known. This paper examines the role of the scalar-parameter exponential model for obtaining approximate probabilities and approximate confidence levels, and then addresses the extension for the vector-parameter exponential model.

We introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Ré nyi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.

The spectrum of arbitrary graph of finite order the exponential growth of the resolvent of graph G is one of the most investigated object during the last 50 years. In particular, the resolvent matrix is a matrix with property that all of its eigenvalues are outside the spectra of G. In this paper, we study the exponential growth of the resolvent of graph G. The exponential growth of resolvent energy of graph G was investigated.