Likelihood Ratio Type Test for Linear Failure Rate Distribution vs. Exponential Distribution

The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and the powers of the test statistic are developed

Estimations on the Generalized Exponential Distribution Using Grouped Data

Classical and Bayesian estimators are obtained for the shape parameter of the Generalized-Exponential distribution under grouped data. In Bayesian estimation, three types of loss functions are considered: the Squared Error loss function which is classified as a symmetric function, the LINEX and Precautionary loss functions which are asymmetric. These estimators are compared with the corresponding estimators derived from un-grouped data empirically using Monte-Carlo simulation

Posterior accuracy and calibration under misspecification in Bayesian generalized linear models

Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize the impact of potential misspecification. We perform a large-scale simulation study on double-bounded and lower-bounded response data where we systematically vary both true and assumed likelihoods and links. In contrast to previous studies, we also study posterior calibration and uncertainty metrics in addition to point-estimate accuracy. Our results indicate that certain likelihoods and links can be remarkably robust to misspecification, performing almost on par with their respective true counterparts. Additionally, normal likelihood models with identity link (i.e., linear regression) often achieve calibration comparable to the more structurally faithful alternatives, at least in the studied scenarios. On the basis of our findings, we provide practical suggestions for robust likelihood and link choices in GLMs

JMASM22: A Convenient Way Of Generating Normal Random Variables Using Generalized Exponential Distribution

A convenient method to generate normal random variable using a generalized exponential distribution is proposed. The new method is compared with the other existing methods and it is observed that the proposed method is quite competitive with most of the existing methods in terms of the K − S distances and the corresponding p-values