Likelihood ratio tests (LRTs) for comparing several independent gamma distributions with respect to shape parameters, scale parameters, and means are derived. The LRT for testing homogeneity of several gamma distributions is also derived. Extensive simulation studies indicate that the null distributions of the LRT statistics for all four problems depend on the parameters only weakly, and for pr...

This paper aims to address the problem of profiling human activities captured in surveillance videos for the applications of online normal human activity recognition and anomaly detection. A novel framework is developed for automatic human activity modeling and online anomaly detection without any manual labeling of the training dataset. The framework consists of the following key components: 1...

1 Likelihood Ratio Test Let X1, ..., Xn be a random sample from a distribution with pdf f(x|θ) where θ is some one dimensional (unknown) parameter. Suppose we want to test the null hypothesis, H0, that θ = θ0 against the alternative hypothesis, Ha, that θ = θ0. Assume the same regularity conditions hold as in the MLE theory. Then likelihood ratio test (LRT) statistic is λ(x) = L(θ0|x) L(θ̂ML|x) ...

In this paper we show how the present day fast computer could solve non-standard old statistical problems. In most cases statisticians work with approximations of test statistics distributions, and then use respective statistical tables. When approximations do not work the problem is usually tabled. We propose such simulation approach which we do believe could be helpful in many case. The probl...

Abstract: In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension is large compared to the sample size. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tes...

For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis and their limiting distributions under the null hypothesis were proved to be chi-square distributions as n goes to in...

The Wilks’ Lambda Statistic (likelihood ratio test, LRT) is a commonly used tool for inference about the mean vectors of several multivariate normal populations. However, it is well known that the Wilks’ Lambda statistic which is based on the classical normal theory estimates of generalized dispersions, is extremely sensitive to the influence of outliers. A robust multivariate statistic for the...

The presence of toxic substances such as persistent organic pollutants (POPs) in the environment, and in organisms including humans, is a serious public health and environmental problem, even at low levels and poses a challenging scientific problem. The Stockholm Convention on POPs (SC) entered into force in 2004 and is a large international effort under the United Nations Environment Programme...

Cost-effective public transit options suitable for serving all demand levels include: bus service in mixed traffic, bus service in reserved lane, transitway/buswdy, light rail transit (LRT) (segregated right of way), intermediate capacity advanced light rail transit (ALRT), and heavy rail rapid transit. This classification of transit options takes into account right-of-way access (that is, mixe...

A new method is required for change-point testing of precipitation data that is capable of applying valid precipitation models. First, stochastic precipation models are researched and classified. Typically, the occurrence of rain is modeled using a two-state, first-order Markov chain, and the intensity of rain is modeled using a two-parameter gamma distribution. Using the likelihood ratio test ...