In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterization of the uniform distribution. Asymptotic theory for the simple hypothesis case is provided in a Hilbert-Space setting, including the asymptotic null distribution as well as values for the first four cumulants of this distribution, which are used to fit a Pearson system of distributions as an approximation to the limit distribution. Numerical results indicate that the null distribution of the test converges quickly to its asymptotic distribution, making the critical values obtained using the Pearson system particularly useful. Consistency of the test is shown against any fixed alternative distribution and we derive the limiting behaviour under fixed alternatives with an application to power approximation. We demonstrate the applicability of the newly proposed test when testing composite hypotheses. A Monte Carlo power study compares the finite sample power performance of the newly proposed test to existing omnibus tests in both the simple and composite hypothesis settings. This power study includes results related to testing for the uniform, normal, Pareto and gamma distributions. The empirical results obtained indicate that the test is competitive. An application of the newly proposed test in financial modelling is also included.

We propose a new L²‐type goodness‐of‐fit test for the family of beta distributions based on a conditional moment characterization. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.

We propose and study new goodness-of-fit tests for the Rayleigh distribution based on a characterization involving a conditional expectation. The asymptotic properties of the tests are explored and the performance of the new tests are evaluated and compared to that of existing tests by means of a Monte Carlo study. It is found that the newly proposed tests perform satisfactory compared to the competitor tests.

The Rayleigh distribution has recently become popular as a model for a range of phenomena. As a result, a number of goodness-of-fit tests have been developed for this distribution. In this paper, we provide the first overview of goodness-of-fit tests for the Rayleigh distribution and compare these tests in a Monte-Carlo study to identify the tests that provide the highest powers against a wide range of alternatives. Our findings suggest that two recently developed tests as well as a test based on the Laplace transform and a test based on the Hellinger distance are the better performing tests.

Classification requires labelling large sets of data, which is often a time-consuming and expensive process. Active learning is a machine learning technique that has gained popularity in recent years due to its ability to effectively reduce the amount of labelled data required to train accurate models. The success of the active learner heavily relies on the selection of the initial points to initialise the active learning process. In this paper, we compare the performance of the traditional random sampling approach to the maximin Latin Hypercube sampling, conditioned Latin Hypercube sampling, and a modified Latin Hypercube sampling procedure for initialising active learning for the estimation of the logistic regression in binary classification problems. We show that the Latin Hypercube sampling designs outperform random sampling for all the performance measures evaluated. The results are demonstrated using simulated data sets and an actual case study. Specifically, the conditioned Latin hypercube sampling design exhibits high prediction accuracy using a smaller sample size for both heterogeneous and homogeneous classes. In contrast, the modified Latin hypercube sampling design yields the smallest variance of prediction across varying initial sample sizes for both homogeneous and heterogeneous classes. Furthermore, principal component analysis indicates that approximately 10\% of the data is required to develop an accurate and precise logistic regression classifier.