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This article presents a novel and powerful goodness-of-fit test specifically designed for the Cauchy distribution. The motivation behind our research stems from the need for a more accurate and robust method to assess the fit of the Cauchy distribution to data. This distribution is known for its heavy tails and lack of finite moments. To compute the proposed test statistic, we utilize the maximum likelihood estimators of the unknown parameters, ensuring the test efficiency and reliability. In addition, Monte Carlo simulations are employed to obtain critical points of the test statistic for different sample sizes, enabling precise determination of the threshold for rejecting the null hypothesis. To assess the performance of the proposed test, we conduct power comparisons against several well-known competing tests, considering various alternative distributions. Through extensive simulations, we demonstrate the superiority of our test in the majority of the cases examined, highlighting its effectiveness in distinguishing departures from the Cauchy distribution. The contributions of our study are twofold. Firstly, we introduce a novel goodness-of-fit test tailored specifically for the Cauchy distribution, taking into account its unique characteristics. By incorporating the maximum likelihood estimate and employing Monte Carlo simulations, our test offers improved accuracy and robustness compared to existing methods. Furthermore, we provide practical validation of the proposed test through the analysis of a financial dataset. The application of the test to real-world data underscores its relevance and applicability in practical scenarios. [ABSTRACT FROM AUTHOR]

The Lindley distribution may serve as a useful reliability model. Applications of this distribution are presented in statistical literature. In this article, goodness of fit tests for the Lindley distribution based on the empirical distribution function (EDF) are considered. In order to compute the test statistics, we use the maximum likelihood estimate (MLE) suggested by Ghitany et al. (2008), which is simple explicit estimator. Critical points of the proposed test statistics are obtained by Monte Carlo simulation. Power comparisons of the considered tests are carried out via simulations. Finally, two illustrative examples are presented and analyzed. [ABSTRACT FROM AUTHOR]

Abstract In this article, based on progressive type-II censored competing risks data with binomial removals, a constant-stress accelerated life testing is discussed when the lifetime of experiment units follows the Pareto distribution. Under the assumption that the failure time of each cause is statistically independent, the estimation of unknown parameters is obtained by maximum likelihood estimation and Bayesian estimators under symmetric and asymmetric loss functions. The corresponding confidence and credible intervals are constructed with approximation theory, bootstrap method, and MCMC technique respectively. Additionally, the log-linear model is established for the life test and two goodness-of-fit test statistics are constructed. Finally, a simulation study is carried out for the power analysis of different censoring ratio schemes and the numerical results verify the feasibility of the constructed test statistics for the censored data with competing risks. [ABSTRACT FROM AUTHOR]

In this paper, the problem of goodness of fit test for the inverse Rayleigh distribution based on progressively Type-II censored samples is studied. We develop two test statistics via entropy and propose one new non-entropy test statistic via a pivotal method. We also study the properties of these test statistics. Critical values are obtained by simulations. Then, we do power analysis of these test statistics against various alternatives under different censoring schemes. We conclude that the tests we proposed perform well against various alternatives, especially for non-monotone hazard alternatives. Finally, one real data set is analyzed. [ABSTRACT FROM AUTHOR]

The Lindley distribution may serve as a useful reliability model. Applications of this distribution are presented in statistical literature. In this article, a powerful goodness of fit test for the Lindley distribution is proposed. In order to compute the proposed test statistic, we use the maximum likelihood estimate (MLE) suggested by Ghitany et al. (2008), which is simple explicit estimator. By Monte Carlo simulation, critical points of the proposed test statistic for different sample sizes are obtained. Power values of the proposed test are compared with the competing tests against various alternatives via simulations. Finally, two real data are presented and analyzed. [ABSTRACT FROM AUTHOR]

The aim of this article is to review existing goodness-of-fit tests for the exponential distribution under progressive Type-II censoring and to provide some new ideas and adjustments. In particular, we consider two-parameter exponentially distributed random variables and adapt the proposed test procedures to our scenario if necessary. Then, we compare their power by an extensive simulation study. Furthermore, we propose five new test procedures that provide reasonable alternatives to those already known. [ABSTRACT FROM AUTHOR]

The manufacturing sector accounts for a high share of global electrical energy consumption and CO2 emissions, and therefore, the environmental impact of production processes is being more and more investigated. An analysis of power and energy consumption in friction stir welding processes can contribute to the characterization of the process from a new point of view and also provide useful information about the environmental impact of the process. An in-depth analysis of electrical energy demand of friction stir welding is here proposed. Different machine tool architectures, including an industrial dedicated machine, have been used to weld aluminum and steel sheets under different process conditions. The influence of tool rotation and feed rate was investigated. A power study, with breakdown analysis, was carried out to identify the contribution of the main sub-units and to determine the total demand. Different setups have been analyzed in order to identify the conditions resulting in the highest energy and mechanical efficiency. Potential control strategies for energy consumption reduction of FSW process are proposed. [ABSTRACT FROM AUTHOR]

The exponential distribution has been used in life-testing and reliability studies. In this article, we first express the entropy of Type-I hybrid censoring scheme in terms of hazard function and provide an estimate of the entropy of Type-I hybrid censored data. Then, we construct a goodness-of-fit test statistic based on Kullback-Leibler information for Type-I hybrid censored data. The test statistic is used to test for exponentiality. A Monte Carlo simulation is conducted to obtain the power of the proposed test against various alternatives. Finally, a data example is presented for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this article, we propose a new approach to testing exponentiality for Type-II censored samples. Our method converts the original observations into transformed data which follow from a special distribution. It is shown that the proposed tests do not depend on the scale parameter of the exponential distribution and hence the tests are exact. Power performance of the proposed tests is compared with the existing tests against various alternatives. The results are impressive and the proposed tests have higher power than the competing tests. Finally, two real data from reliability literature as illustrate examples are presented.

The PoweR package aims to help obtain or verify empirical power studies for goodnessof-fit tests for independent and identically distributed data. The current version of our package is only valid for simple null hypotheses or for pivotal test statistics for which the set of critical values does not depend on a particular choice of a null distribution (and on nuisance parameters) under the non-simple null case. We also assume that the distribution of the test statistic is continuous. As a reproducible research computational tool it can be viewed as helping to simply reproducing (or detecting errors in) simulation results already published in the literature. Using our package helps also in designing new simulation studies. The empirical levels and powers for many statistical test statistics under a wide variety of alternative distributions can be obtained quickly and accurately using a C/C++ and R environment. The parallel package can be used to parallelize computations when a multicore processor is available. The results can be displayed using LATEX tables or specialized graphs, which can be directly incorporated into a report. This article gives an overview of the main design aims and principles of our package, as well as strategies for adaptation and extension. Hands-on illustrations are presented to help new users in getting started.

In many life-testing and reliability experiments, data are often censored in order to reduce the cost and time associated with testing and since the conventional Type-I and Type-II censoring schemes are not flexible enough, progressive censoring is developed by researchers. In this article, we develop a general goodness of fit test by using a new estimate of Kullback–Leibler information based on progressively Type-II censored data. Consistency and other properties of the proposed test are shown. Then, we use the proposed test statistic to test for exponentiality based on progressively Type-II censored data. The power values of the proposed test under different progressively Type-II censoring schemes are computed, through Monte Carlo simulations. It is observed that the proposed test is quite powerful in compared with the test proposed by Balakrishnan et al. (2007). Two real datasets from progressive censoring literature are finally presented for illustrative purpose. [ABSTRACT FROM AUTHOR]

The exponential distribution is commonly used to model and examine lifetime data. When applying the exponential model, it is critical to develop efficient goodness of fit tests. In this article, we first propose some new entropy estimators for Type-II censored data and then introduce some goodness of fit test statistics for the exponential distribution based on Type-II censored data using different entropy estimators. The critical values of the tests do not depend on the scale parameter of the exponential distribution and therefore the proposed tests are exact. The critical values and powers of the tests are obtained. The Monte Carlo simulation study indicates that the proposed tests have higher powers than competing tests against the alternatives with monotone increasing hazard functions. Real-life data examples demonstrate the applicability of the proposed tests in practice. [ABSTRACT FROM AUTHOR]

The logistic distribution is one of the fundamental distribution and is widely used for describing model growth curves in survival analysis and biological studies. Applications of this distribution are presented in statistical literature. In this article, goodness of fit tests for the logistic distribution based on the empirical distribution function (EDF) are considered. In order to compute the test statistics, because the MLEs cannot be obtained explicitly, we use the approximate maximum likelihood estimates (AMLEs) suggested by Balakrishnan and Cohen (1990), which are simple explicit estimators. Power comparisons of the considered tests are carried out via simulations. Finally, two illustrative examples are presented and analyzed. [ABSTRACT FROM AUTHOR]

In this article, we study a goodness-of-fit (GOF) test in the presence of length-biased sampling. For this purpose, we introduce a smoothed estimator of distribution function (d.f.) and we investigate its asymptotic behaviors, such as uniform consistency and asymptotic normality. Based on this estimator, we define a one-sample Kolmogorov type of GOF test for length-biased data. We conduct Monte Carlo simulations to evaluate the performance of the proposed test statistic and compare it with the one-sample Kolmogorov type of GOF test obtained by the non smoothed estimator of d.f. [ABSTRACT FROM AUTHOR]

In this article, the general test statistic introduced by Alizadeh Noughabi and Balakrishnan [Goodness of fit using a new estimate of Kullback-Leibler information based on Type II censored data. IEEE Trans Reliab. 2015;64:627–635.] is applied for testing goodness of fit of lifetime distributions based on Type II censored data. The test statistic is constructed based on an estimate of Kullback–Leibler (KL) information. We investigate the properties of the proposed test statistic such as the test statistic is nonnegative, just like KL information. We apply this test statistic to following distributions: Exponential, Weibull, Log-normal and Pareto. The critical values and Type I error of the proposed tests are obtained. It is shown that the proposed tests have an excellent Type I error and hence can be used confidently in practice. Then, by Monte Carlo simulations, the power values of the proposed tests are computed against several alternatives and compared with those of the existing tests. Finally, some real-world reliability data are used for illustrative purpose. [ABSTRACT FROM PUBLISHER]

Verification of regression models is primarily based on analysis of error terms and constitutes one of the most important steps in applied regression analysis. In cross-sectional models, the error terms are typically heteroskedastic, while in time series regressions the errors are often affected by serial correlation. Consequently, in this paper, we focus on Monte Carlo simulations applied to explore the power of several tests of homogeneity and tests for presence of autocorrelation. In the past decades, the computational power has increased significantly to allow the benefit of simulation from exact distributions, which are not defined explicitly. We will discuss 1) testing of homogeneity for a given number of components in the exponential mixture approximated by subpopulations and 2) simulation of power in several commonly used tests of autocorrelation. For the first case, we consider exact likelihood ratio test (ELR) and exact likelihood ratio test against the alternative with two-component subpopulation (ELR2). In the second case, we consider the Durbin-Watson, Durbin h, Breusch-Godfrey, Box-Pierce and Ljung-Box tests of 1st order serial correlation and the runs test of randomness in two different types of linear regression models.

The aim of this paper is to present and discuss the power of the exact likelihood ratio homogeneity testing procedure of the number of components k in the exponential mixture. First we present the likelihood ratio test for homogeneity (ELR), the likelihood ratio test for homogeneity against two-component exponential mixture (ELR2), and finally the likelihood ratio test for homogeneity against three-component exponential mixture (ELR3). Comparative power study of mentioned homogeneity tests against three-component subpopulation alternative is provided. Therein we concentrate on various setups of the scales and weights, which allow us to make conclusions for generic settings. The natural property is observed, namely increase of the power of exact likelihood ratio ELR, ELR2 and ELR3 tests with scale parameters considered in the alternative. We can state that the differences in power of ELR, ELR2 and ELR3 tests are small – therefore using of the computationally simpler ELR2 test is recommended for broad usage rather than computationally more expensive ELR3 test in the cases when unobserved heterogeneity is modelled. Anyhow caution should be taken before automatic usage of ELR3 in more informative settings, since the application of automatic methods hoping that the data will enforce its true structure is deceptive. Application of obtained results in reliability, finance or social sciences is straightforward.

In this article, we use cumulative residual Kullback-Leibler information (CRKL) and cumulative Kullback-Leibler information (CKL) to construct two goodness-of-fit test statistics for testing exponentiality with progressively Type-II censored data. The power of the proposed tests are compared with the power of goodness-of-fit test for exponentiality introduced by Balakrishnan et al. (2007). We show that when the hazard function of the alternative is monotone decreasing, the test based on CRKL has higher power and when the hazard function of the alternative is non-monotone, the test based on CKL has higher power. But, when it is monotone increasing the power difference between test based on CKL and their proposed test is not so remarkable. The use of the proposed tests is shown in an illustrative example. [ABSTRACT FROM AUTHOR]

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We propose a class of flexible non-parametric tests for the presence of dependence between components of a random vector based on weighted Cramér–von Mises functionals of the empirical copula process. The weights act as a tuning parameter and are shown to significantly influence the power of the test, making it more sensitive to different types of dependence. Asymptotic properties of the test are stated in the general case, for an arbitrary bounded and integrable weighting function, and computational formulas for a number of weighted statistics are provided. Several issues relating to the choice of the weights are discussed, and a simulation study is conducted to investigate the power of the test under a variety of dependence alternatives. The greatest gain in power is found to occur when weights are set proportional to true deviations from independence copula. [ABSTRACT FROM PUBLISHER]

In goodness-of-fit testing based on Type-II right censored samples, mainly either classical tests are applied to transformed samples, which can be considered as full samples under the null hypothesis, or modifications of the tests are applied to the original samples. Results of an extensive simulation study are presented and discussed in order to compare the different approaches and tests by means of powers against beta alternatives. Depending on the beta parameters, illustrative plots lead to recommended tests in given situations, where there is some prior belief about the size of these parameters in the alternative. Moreover, the effects of adding artificial realizations via random dilation are examined. [ABSTRACT FROM PUBLISHER]

In this article, a general goodness of fit test is developed by using a new estimate of Kullback-Leibler (KL) information based on Type-II censored data. The proposed test is consistent, and the test statistic is nonnegative, just like KL information. Then, the test statistic is used to test for exponentiality based on Type-II censored data. Through a simulation study, power values of the proposed test are compared with some prominent existing tests. A real-life data analysis is finally presented for illustrative purpose. [ABSTRACT FROM AUTHOR]

There are multiple tests of homogeneity of binomial proportions in the statistics literature. However, when working with sparse data, most test procedures may fail to perform well. In this article we review nine classical and recent testing procedures, including the standard Pearson and likelihood ratio tests; exact conditional and unconditional tests; tests based on moment matching chi-squared approximations; a recently proposed test based on a normal approximation in an asymptotic framework for sparse data; and a recent test based on higher order moment corrections using an Edgeworth approximation. For each test we review its theoretical underpinning, and show how to calculate the P-value. Most of the P-values can be readily calculated in a statistical computing software package such as R. We compare type I error probability and power via simulation. As expected, none of the procedures uniformly outperforms the others in terms of type I error probability and power, but we can make some recommendations based on our empirical results. In particular, we indicate scenarios in which certain otherwise reasonable test procedures can perform inadequately.

Abstract: Production processes, as used for discrete part manufacturing, are responsible for a substantial part of the environmental impact of products, but are still poorly documented in terms of environmental impact. The present paper proposes an energy analysis of single point incremental forming processes (SPIF). The electrical energy consumption of two different setups have been considered and compared. In particular the power demand of one of the most used machine tools architecture able to perform SPIF process, namely a CNC milling machine, has been measured. The obtained results have been compared with the ones obtained for an innovative high speed incremental forming processes performed on CNC-turning machine. In order to find out the most energy efficient solution working cycle time study and power study were performed. [Copyright &y& Elsevier]

For classical goodness-of-fit tests as well as for their modified versions in case of Type-II right censored data, results of a simulation study are presented, where the powers of the tests under consideration against beta alternatives are illustrated in informative, user-oriented plots that offer the possibility to directly choose the best test statistic in a concrete situation, when some prior belief about the alternative is available. The behavior of powers of respective statistical tests as functions of beta parameters is examined and discussed. [ABSTRACT FROM AUTHOR]

Testing exponentiality has long been an interesting issue in statistical inferences. In this article, we introduce a new measure of distance between two distributions that is similar Kullback–Leibler divergence, but using the distribution function rather than the density function. This new measure is based on the cumulative residual entropy. Based on this new measure, a consistent test statistic for testing the hypothesis of exponentiality against some alternatives is developed. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for the test statistics. Also, by means of Monte Carlo simulations, the power of the proposed test under various alternative is compared with that of other tests. Finally, we found that the power differences between the proposed test and other tests are not remarkable. The use of the proposed test is shown in an illustrative example. [ABSTRACT FROM AUTHOR]

The empirical likelihood (EL) technique is a powerful nonparametric method with wide theoretical and practical applications. In this article, we use the EL methodology in order to develop simple and efficient goodness-of-fit tests for normality based on the dependence between moments that characterizes normal distributions. The new empirical likelihood ratio (ELR) tests are exact and are shown to be very powerful decision rules based on small to moderate sample sizes. Asymptotic results related to the Type I error rates of the proposed tests are presented. We present a broad Monte Carlo comparison between different tests for normality, confirming the preference of the proposed method from a power perspective. A real data example is provided. [ABSTRACT FROM AUTHOR]

We consider testing for an unobservable normal distribution with unspecified mean and variance. It is only possible to observe the counts in groups with boundaries specified before sighting the data. On the basis of a small power study, we recommend the usual X2 test be used as an omnibus test, augmented by informal examination of the first two non-zero components of X2. We also recommend use of maximum likelihood and method of moments estimation. [ABSTRACT FROM AUTHOR]

There exist now a number of statistical methods for detecting differential gene expression in experiments with microarray data. In trials under two conditions, a version of the two-sample t statistic is usually used. However, the problem of estimating the power for these tests has so far been insufficiently studied. In this paper, we propose a method to calculate the power of the robust t test for detecting differential gene expression in experiments with twins. We discuss also the results of the implementation of this method to simulated data. [ABSTRACT FROM AUTHOR]

The inverse Gaussian family is widely used for modeling positively skewed measurements. In this note, we present an entropy characterization of the inverse Gaussian family and use it to construct a goodness-of-fit test for ascertaining appropriateness of such models. This test is consistent against all alternatives without a singular component and has good power properties. [Copyright &y& Elsevier]