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...

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping whe...

Statistical prediction plays an important role in many decision processes, such as university budgeting (depending on the number of students who will enroll), capital remaining lifetime a fleet systems), needed amount cash reserves for warranty expenses returns), and whether product recall is potentially life-threatening failures). In statistical inference, likelihood ratios have long history u...

This paper considers the asymptotic distribution of the likelihood ratio statistic T for testing a subset of parameter of interest θ, θ = (γ, η), H(0) : γ = γ(0), based on the pseudolikelihood L(θ, ϕ̂), where ϕ̂ is a consistent estimator of ϕ, the nuisance parameter. We show that the asymptotic distribution of T under H(0) is a weighted sum of independent chi-squared variables. Some sufficient co...

Berk and Jones (1979) introduced a goodness of fit test statistic Rn which is the supremum of pointwise likelihood ratio tests for testing H0 : F (x) = F0(x) versus H1 : F (x) = F0(x). They showed that their statistic does not always converge almost surely to a constant under alternatives F , and, in fact that there exists an alternative distribution function F such Rn →d supt>0 N(t)/t where N ...

Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583) proposed an approximate likelihood ratio (ALR) test of the null hypothesis that a normal mean vector equals a null vector against the alternative that all of its components are nonnegative with at least one strictly positive. This test is useful for comparing a treatment group with a control group on multiple endpoints, and the data from t...

Early detection of disease outbreaks is of paramount importance to implementing intervention strategies to mitigate the severity and duration of the outbreak. We build methodology that utilizes the characteristic profile of disease outbreaks to reduce the time to detection and false positive rate. We model daily counts through a Poisson distribution with additive background plus outbreak compon...