Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

This paper investigates the relationship between the loss function, the type of regularization, and the resulting model sparsity of discriminatively-trained multiclass linear models. The effects on sparsity of optimizing log loss are straightforward: L2 regularization produces very dense models while L1 regularization produces much sparser models. However, optimizing hinge loss yields more nuan...

In this work, a three-parameter Weibull Inverse Rayleigh (WIR) distribution is proposed. The new WIR an extension of one-parameter that incorporated transformation the and Log-logistic as quantile function. statistical properties such function, order statistic, monotone likelihood ratio property, hazard, reverse hazard functions, moments, skewness, kurtosis, linear representation proposed were ...

Through assembling the navigation parameters as matrix Lie group state, corresponding inertial system (INS) kinematic model possesses a group-affine property. The logarithm of state estimation error satisfies log-linear autonomous differential equation. These models are still applicable even with arbitrarily large initial errors, which is very attractive for INS alignment. However, in existing ...

This paper presents a Bayesian additive “correction” to the familiar quadratic loss biasplus-variance formula. It then discusses some other loss-function-specific aspects of supervised learning. It ends by presenting a version of the bias-plus-variance formula appropriate for log loss, and then the Bayesian additive correction to that formula. Both the quadratic loss and log loss correction ter...

Most error log analysis studies perform a statistical fit to the data assuming a single underlying error process. This paper presents the results of an analysis that demonstrates the log is composed of at least two error processes: transient and intermittent. The mixing of data from multiple processes requires many more events to verify a hypothesis using traditional statistical analysis. Based...