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The reformed Basel framework has left value at risk (VaR) as a basic tool of validating risk models. Within this framework, VaR independence tests have been regarded as critical to ensuring stability during periods of financial turmoil. However, until now, there is no consent among researchers regarding the choice of the appropriate test. The available procedures are either inaccurate in finite samples or need to rely on Monte Carlo simulations. To remedy these problems, we propose a new method for testing VaR models, based on the distribution of the number of runs. It outperforms the existing methods in two main aspects: First, it is exact in finite samples and thus allows for perfect control over the Type 1 error; second, its distribution is available in a closed form, so it does not require simulations before implementation. We show that it is the most adequate current procedure for testing low‐level VaR series, which corresponds to today's regulatory standards. [ABSTRACT FROM AUTHOR]

Recently, Alizadeh and Shafaei (2023) introduced some estimators for varentropy of a continuous random variable. The present article applies these estimators and construct some tests of fit for Inverse Gaussian distribution. Percentage points and type I error of the new tests are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests.

Recently, Alizadeh and Shafaei [Alizadeh Noughabi H, Shafaei Noughabi M. Varentropy estimators with applications in testing uniformity. J Stat Comput Simul. 2023;93:2582–2599] introduced some estimators for varentropy of a continuous random variable. The present article applies these estimators and construct some tests for normality. Percentage points of the new test statistics are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests. [ABSTRACT FROM AUTHOR]

Two-sample tests are widely used in hydrologic and climate studies to investigate whether two samples of a variable of interest could be considered drawn from different populations. Despite this, the information on the power (i.e., the probability of correctly rejecting the null hypothesis) of these tests applied to hydroclimatic variables is limited. Here, this need is addressed considering four popular two-sample tests applied to daily and extreme precipitation, and annual peak flow series. The chosen tests assess differences in location (t-Student and Wilcoxon) and distribution (Kolmogorov–Smirnov and likelihood-ratio). The power was quantified through Monte Carlo simulations relying on pairs of realistic samples of the three variables with equal size, generated with a procedure based on suitable parametric distributions and copulas. After showing that differences in sample skewness are monotonically related to differences in spread, power surfaces were built as a function of the relative changes in location and spread of the samples and utilized to interpret three case studies comparing samples of observed precipitation and discharge series in the U.S. It was found that (1) the t-Student applied to the log-transformed samples has the same power as the Wilcoxon test; (2) location (distribution) tests perform better than distribution (location) tests for small (moderate-to-large) differences in spread and skewness; (3) the power is relatively lower (higher) if the differences in location and spread or skewness have concordant (discordant) sign; and (4) the power increases with the sample size but could be quite low for tests applied to extreme precipitation and discharge records that are commonly short. This work provides useful recommendations for selecting and interpreting two-sample tests in a broad range of hydroclimatic applications. [ABSTRACT FROM AUTHOR]

Recently, Alizadeh and Shafaei (2023) introduced some esti- mators for the varentropy of a continuous random variable. The present article applies these estimators and constructs some tests of fit for Inverse Gaussian distribution. Percentage points and type I error of the new tests are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests [ABSTRACT FROM AUTHOR]

The Lindley distribution may serve as a useful reliability model. In this article, we propose a goodness of fit test for the Lindley distribution based on the empirical likelihood (EL) ratio. The properties of the proposed test are stated and the critical values are obtained by Monte Carlo simulation. Power comparisons of the proposed test with some known competing tests are carried out via simulations. Finally, an illustrative example is presented and analyzed. [ABSTRACT FROM AUTHOR]

In this study, the effect of multicollinearity, which is defined as high correlation, on the type I error rate and test power of the binary logistic regression models were studied. To do this, one dependent variable that consists of 1 and 2 and four continuous independent variables that were randomly drawn from the standardized normal distribution were taken into consideration in the constructed binary logistic regression model. To calculate the type I error rates and test power, the simulation study was performed 100.000 times. The simulation study repeated for the sample sizes of 10, 20, 30 and 40 the various degrees of correlations, namely 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90%. In order to calculate test power, differences (δ) were created between population means by adding to the mean of the second population in standard deviation units as 0.5, 1.0, 1.5 and 2.0, respectively. The simulation runs exhibited that the increasing degree of multicollinearity among independent variables had no influence on type I error rates, provided that the sample size should not be smaller than 30. The power of the binary logistic regression was least affected by the increasing degrees of multicollinearity when the sample size is 10 and there is a 0.5δ difference between population means. The fact that there was a marked decline in test power with rising multicollinearity for all sample sizes clarified that the binary logistic regression was most powerful if there is no strong multicollinearity among independent variables when there is a 1.0δ difference between population means. The negative impact of the rising degrees of multicollinearity on the test power can be avoided if the number of observations is sufficiently large and if the populations were satisfactorily separated from each other. [Med-Science 2023; 12(4.000): 1180-4]

AbstractIn survival analysis and reliability studies the Lindley distribution has been widely used. In this article, we introduce a new goodness of fit test for the Lindley distribution based on an estimate of the Gini index. The asymptotic distribution of the new test statistic is investigated. The unknown parameter of the Lindley distribution is estimated by the maximum likelihood estimator. The critical points and the actual sizes of the test are obtained by Monte Carlo simulations. A power comparison study of the existing tests is performed. It is shown that the Gini index-based test that we proposed performs well by comparing its powers with that of other tests. A real-life data analysis is finally presented for illustrative purpose. [ABSTRACT FROM AUTHOR]

The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function. In order to compute the test statistics, parameters of the Inverse Gaussian distribution are estimated by maximum likelihood estimators (MLEs), which are simple explicit estimators. Critical points and the actual sizes of the tests are obtained by Monte Carlo simulation. Through a simulation study, power values of the tests are compared with each other. Finally, an illustrative example is presented and analyzed. [ABSTRACT FROM AUTHOR]

While power reduction during testing is necessary for today's low-power devices, it also lowers test costs. Scan-based methods are the most widely used approach for testing integrated circuits (IC). Test vectors are shifted into and out of scan chains bit by bit during shift operation. The time required for shift operation dominates the test time. With the geometries shrinking (7 nm→5 nm→3 nm→1.8 nm), ICs are required to be tested for newer defects, increasing test time. The most effective way to reduce test time for scan operation is to increase the frequency of the shift operation. Reduction in shift power enables scan operation to be performed with increased frequency, reducing test time, and test cost. This paper presents a survey of techniques proposed recently for shift power reduction. Various techniques, including special flip-flop usage, segmentation, reordering, and low-pass filter, are being reviewed. The techniques are organized based on main attributes to underscore their similarities and differences. Pros and cons in terms of complexities involved in their implementation are discussed. We believe this paper will provide a point of reference for further studies in scan shift power reduction and will be helpful to both industry and academia. [ABSTRACT FROM AUTHOR]

In this study, the effect of multicollinearity, which is defined as high correlation, on the type I error rate and test power of the binary logistic regression models were studied. To do this, one dependent variable that consists of 1 and 2 and four continuous independent variables that were randomly drawn from the standardized normal distribution were taken into consideration in the constructed binary logistic regression model. To calculate the type I error rates and test power, the simulation study was performed 100.000 times. The simulation study repeated for the sample sizes of 10, 20, 30 and 40 the various degrees of correlations, namely 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90%. In order to calculate test power, differences (δ) were created between population means by adding to the mean of the second population in standard deviation units as 0.5, 1.0, 1.5 and 2.0, respectively. The simulation runs exhibited that the increasing degree of multicollinearity among independent variables had no influence on type I error rates, provided that the sample size should not be smaller than 30. The power of the binary logistic regression was least affected by the increasing degrees of multicollinearity when the sample size is 10 and there is a 0.5δ difference between population means. The fact that there was a marked decline in test power with rising multicollinearity for all sample sizes clarified that the binary logistic regression was most powerful if there is no strong multicollinearity among independent variables when there is a 1.0δ difference between population means. The negative impact of the rising degrees of multicollinearity on the test power can be avoided if the number of observations is sufficiently large and if the populations were satisfactorily separated from each other. [ABSTRACT FROM AUTHOR]

ABSTRACT In this study, some transformation methods that are applied when the assumptions of analysis of variance are not met are evaluated in terms of type I error rate and the test power, under circumstances with different distributions, number of groups, number of observations, variance ratios, and different standard deviation differences. The data set used in the study consisted of random numbers generated from N (0,1), and χ2(3) distributions using the random function of the Numpy library in the Python programming language. The logarithmic, square root and root transformations were evaluated on ANOVA based on simulation combinations. It was observed that the transformation techniques of taking the square root after adding 0.5 and 0.375 to the data were relatively more reliable compared to other transformations in terms of type I error rate. However, in every case, type I error rate determined at the beginning of the experiment increased both before and after the transformation was applied. In particular, interestingly, the third and fourth degree root transformations gave better results of test power in the right skewed distribution. In addition, we compared the transformation techniques in question to determine the normality of the data and the homogeneity of variances by a real data.

We propose here a general statistic for the goodness-of-fit test of statistical models. The proposed statistic is constructed based on an estimate of Kullback–Leibler information. The properties of the proposed test are stated and then the established results are used to introduce goodness-of-fit tests for the normal and exponential distributions. A simulation study is carried out for examining the power of the proposed test and to compare it with those of some existing procedures. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can confidently apply in practice. Finally, some illustrative examples are presented and analysed, and concluding comments are made. [ABSTRACT FROM AUTHOR]

Recently, Di Crescenzo and Paolillo [Di Crescenzo A, Paolillo L. Analysis and applications of the residual varentropy of random lifetimes. Probab Eng Informational Sci. 2021;35(3):680–698] and Maadani et al. [Maadani S, Mohtashami Borzadaran GR, Rezaei Roknabadi AH. Varentropy of order statistics and some stochastic comparisons. Commun Stat - Theory Methods. 2021;51(18):6447–6460.] presented the applications of varentropy in reliability theory. The present article introduces some estimators of the varentropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made in terms of the mean squared error. Then, the proposed estimators are applied and some tests for uniformity are constructed. Percentage points and power values of the tests against seven alternatives are reported. The results of a simulation study show that the tests have good performance in terms of power. [ABSTRACT FROM AUTHOR]

In this study, we compared the Student's t-test, Welch's t-test, and Mann-Whitney U test, in terms of their type I error rate and statistical power when the assumptions of parametric tests are violated in different situations. Materials used in this study, consisted of random numbers generated using the Numpy library in the Python programming language. All random numbers were generated from a normal distribution with N (0, 1) parameters. Balanced and unbalanced experimental conditions were simulated 50 000 times for each combination. The study revealed that, in comparison to other tests, Welch's t - test was particularly more conservative in terms of type I error rate. It was discovered that the Student-t test had higher power values than the Mann-Whitney U test, mainly when only a small sample size of observations was used for the analysis. This simulation study indicated that Welch's t - test is robust for preserving type I error rate when the distribution is normal. Therefore, in practice, the use of Welch t-test is recommended based on the findings of this study. One of the recommendations of this study is that the tests in question should also be evaluated in cases where observations have different distributions. [ABSTRACT FROM AUTHOR]

Recently, extropy as an alternative measure of uncertainty has been widely used in statistical procedures. In this article, we present some properties of the negative cumulative residual extropy and then propose a test for uniformity. An approximation of distribution of the test statistic is derived. The mean, variance and the asymptotic null distribution of the test statistic is presented. Percentage points and power against seven alternatives are reported. The results of a simulation study show the test is competitive in terms of power. Moreover, the proposed statistic is easy to compute and can approximate by the beta distribution. [ABSTRACT FROM AUTHOR]

Some widely used classical tests for homogeneity of variance (Fisher, Link, Cochran, and Bliss–Cochran–Tukey) are considered for the case when the random variable has a symmetric two-side power distribution. The corresponding critical values for the test statistics are obtained. Some comparative analysis of power of the tests is carried out. The case when the null hypothesis assumes a minor random scatter of the variance is considered separately. [ABSTRACT FROM AUTHOR]

The problem of homoscedasticity arises in several fields such as business, education, environments, and medicine, and common question in many statistical analyses. One of the most important tests in this direction is Levene test and its robust version Brown-Forsythe test. The goal of this paper is threefold. The first goal is to propose an expression that enable to develop a graphical way for Levene-Brown-Forsythe tests. The second goal is to derive the sampling distribution of the proposed expression as the generalized beta prime distribution. The third goal is to provide deep insight and understanding where the dispersion effects occur. Simulation study is carried out to study the level of significance and power of the proposed test in comparison with the original Levene-Brown-Forsythe tests. The results are of great values since the proposed method provides (a) powerful visual tool and deep insight for testing homoscedasticity, (b) keeps the size and power of the test similar to Levene-Brown-Forsythe tests, and (c) does not need to pairwise comparisons. Two applications are presented to show the utilities of the proposed method.

Recently, it has been shown that the density based empirical likelihood concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics. In this article, we propose a density based empirical likelihood goodness of fit test for the Cauchy distribution. The properties of the test statistic are stated and the critical points are obtained. Power comparisons of the proposed test with some known competing tests are carried out via simulations. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can confidently apply in practice. Finally, a financial data set is presented and analyzed.

Recurrent event responses are frequently encountered during clinical trials of treatments for certain diseases, such as asthma. The recurrence rates of different treatments are often compared by applying the negative binomial model. In addition, a balanced treatment-allocation procedure that assigns the same number of patients to each treatment is often applied. Recently, a response-adaptive treatment-allocation procedure has been developed for trials with recurrent event data, and has been shown to be superior to balanced treatment allocation. However, this response-adaptive treatment allocation procedure is only applicable for the comparison of two treatments. In this paper, we derive response-adaptive treatment-allocation procedures for trials which comprise several treatments. As pairwise comparisons and multiple comparisons with a control are two common multiple-testing scenarios in trials with more than two treatments, corresponding treatment-allocation procedures for these scenarios are also investigated. The redesign of two clinical studies illustrates the clinical benefits that would be obtained from our proposed response-adaptive treatment-allocation procedures. [ABSTRACT FROM AUTHOR]

To increase the power of the VaR tests, it has been recently proposed to extend the duration-based test class with the geometric-VaR and Gini-coefficient-based tests. These tests, though exhibiting outstanding power properties, have not gained recognition in the industry. A potential reason is the absence of ready-to-use statistical distributions. To remedy this, we inquire into the limiting properties of these tests and derive relevant asymptotic distributions. We also provide a generalized geometric-VaR test and give its distribution. Through the Monte Carlo study, we show the accuracy of our asymptotic procedures in finite samples, and we find these procedures to be relevant for the current Basel standards. Our theoretical results are illustrated by the empirical study that includes data from the current COVID-19 crisis. [ABSTRACT FROM AUTHOR]

We present properties of the cumulative residual entropy and then propose a test for uniformity. An approximation of distribution of the test statistic is derived. The mean, variance, and the asymptotic null distribution of the test statistic are presented. Percentage points and power against seven alternatives are reported. The results of a simulation study show that the test is competitive in terms of power. Moreover, the proposed statistic is easy to compute and can be approximated by the beta distribution. [ABSTRACT FROM AUTHOR]

The results of the extropy of order statistics are applied to constructing a test statistic for symmetry. This test statistic has this advantage that we do not need to estimate the center of the symmetry. Through a simulation study, the power of the test is computed and then compared with the competing tests. The power results show that, for a wide variety of alternative asymmetric distributions, the proposed test is much more powerful than other tests. A real dataset is presented and analyzed. [ABSTRACT FROM AUTHOR]

We introduce a new test for exponentiality against decreasing (increasing) mean residual life alternatives based on a cumulative residual Renyi's entropy of order α. The exact and asymptotic distributions of the test statistic are given. The performance of the proposed test statistic is compared with other constructed tests in the literature using a simulation study. Finally, some numerical examples illustrating the theory are given. [ABSTRACT FROM AUTHOR]

Recently, it has been shown that the density based empirical likelihood concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics. In this article, we propose a density based empirical likelihood goodness of fit test for the Cauchy distribution. The properties of the test statistic are stated and the critical points are obtained. Power comparisons of the proposed test with some known competing tests are carried out via simulations. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can confidently apply in practice. Finally, a financial data set is presented and analyzed. [ABSTRACT FROM AUTHOR]

In this study, one-way ANOM (Analysis of Means) and ANOMTR (Analysis of Means Based on Transformed Ranks) tests were compared in non-normal distributions with homogeneous variances in terms of the Type I error rate and test power. As a result of 100.000 simulation experiments conducted, regardless of the experimental conditions considered, actual Type I error rates occurred in ANOMTR was within the limits of 4.50-5.50%. However, it was observed that actual Type I error rates occurred in ANOM test was generally not within these limits. The ANOM test was found to be affected quite negatively by the kurtosis rather than the skewness of the distribution. As long as the variances were homogeneous, the ANOMTR test has given very reliable results regardless of the shape of the distribution and the number of replications.

Although regulatory standards, currently developed by the Basel Committee on Banking Supervision, anticipate a shift from VaR to ES, the evaluation of risk models currently remains based on the VaR measure. Motivated by the Basel regulations, we address the issue of VaR backtesting and contribute to the debate by exploring statistical properties of the exponential autoregressive conditional duration (EACD) VaR test. We show that, under the null, the tested parameter lies at the boundary of the parameter space, which can profoundly affect the accuracy of this test. To compensate for this deficiency, a mixture of chi-square distributions is applied. The resulting accuracy improvement allows for the omission of the Monte Carlo simulations used to implement the EACD VaR test in earlier studies, which dramatically improves the computational efficiency of the procedure. We demonstrate that the EACD approach to testing VaR has the potential to enhance statistical inference in most problematic cases – for small samples and for those close to the null. [ABSTRACT FROM AUTHOR]

Monitoring the mortality associated with a surgical procedure leads to the proper decision making in a healthcare system. However, the surgical outcomes depend not only on the risk factors of each patient but also on other categorical influential covariates which cannot be easily measured. Ignoring the unmeasured covariates leads to the poor performance of monitoring procedures. To deal with this significant issue, a general Phase-I risk-adjusted cumulative sum control chart is proposed using a combination of accelerated failure time and frailty models to monitor surgical outcomes. Extensive simulation studies are conducted which reveal that the proposed frailty-based CUSUM chart outperforms the simple CUSUM chart. Moreover, the proposed approach performs better than the existing dummy-based CUSUM chart in terms of detection power. Subsequently, the results of a real cardiac surgery dataset indicate that the inclusion of frailty variables in the risk-adjustment model can effectively model the heterogeneity of the surgical data. [ABSTRACT FROM AUTHOR]

Under the Basel III and Basel IV accords, risk model validation remains based on the VaR measure. According to the industry practice, VaR backtesting procedures rely on two likelihood ratio tests, which, in light of the academic research, have been criticized for their unsatisfactory power. This paper aims to show the differences between VaR model evaluation based on the standard likelihood ratio approach and backtesting by means of other econometric methods applicable to the binary VaR failure process. The author decomposed the model evaluation into testing the unconditional coverage, replaced the likelihood ratio with a normal statistic, and in the next stage in order to verify the conditional coverage, employed the Ljung-Box statistic. The study experimentally confirmed the superiority of the proposed procedures over the industry standards. The main contribution, however, is the empirical study designed to demonstrate the practical differences in risk analysis attributable to the choice of the backtesting method. Using data on leading stock market indexes, from various periods, the author showed that the practical conclusions from backtesting diverge markedly due to the test choice. The proposed, more powerful tests, contrary to the standard procedures, allowed for distinguishing distinct models of index behaviour connected with undergoing the financial crises. [ABSTRACT FROM AUTHOR]

Non-inferiority (NI) trials have gained recognition as an effective tool with which to search for substitutes for a standard treatment that is associated with certain undesirable features, such as adverse side-effects, an exorbitant cost, or an extremely complicated therapeutic regimen. Statistical methods have been developed for NI studies with multiple experimental treatments. However, experimental treatments sometimes represent a new treatment with various dose levels, and in such circumstances, identification of the minimum non-inferior dose is a reasonable objective of the trial. Thus, we examine several potential testing procedures with respect to this testing objective. A simulation study is conducted to evaluate their performance, and determination of the sample size is discussed. Two clinical examples are provided to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

The Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other important information and reliability measures. In this paper, some novel properties of the cumulative residual Tsallis entropy are disclosed. Moreover, this entropy measure is applied to testing the uniformity, where the limit distribution and an approximation of the distribution of the test statistic are derived. In addition, the property of stability is discussed. Furthermore, the percentage points and power against seven alternative distributions of this test statistic are presented. Finally, to compare the power of the suggested test with that of other tests of uniformity, a simulation study is conducted.

In this article, we propose some tests of fit based on sample entropy for the composite Gumbel (Extreme Value) hypothesis. The proposed test statistics are constructed using different entropy estimates. Through a Monte Carlo simulation, critical values of the test statistics for various sample sizes are obtained. Since the tests based on the empirical distribution function (EDF) are commonly used in practice, the power values of the entropy-based tests with those of the EDF tests are compared against various alternatives and different sample sizes. Finally, two real data sets are modeled by the Gumbel distribution. [ABSTRACT FROM AUTHOR]

The exponential distribution is widely used in reliability and life testing analysis. In this paper, two tests of fit for the exponential distribution based on Informational Energy and entropy are constructed. Consistency and other properties of the tests are proved. Using a simulation study, critical values of the proposed tests are obtained and then power values of tests are computed and compared with each other against various alternatives. Finally, we apply the tests for time between failures of secondary reactor pumps and waiting times for fatal plane accidents in the USA from 1983 to 1998. [ABSTRACT FROM AUTHOR]

Goodness-of-fit tests are constructed for the two-parameter Birnbaum-Saunders distribution in the case where the parameters are unknown and therefore are estimated from the data. In each test, the procedure starts by computing efficient estimators of the parameters. Then the data are transformed by a normal transformation and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Three classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function and the final class utilizes the Kullback-Leibler information function. All methods are extended to cover the case of generalized three-parameter Birnbaum-Saunders distributions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new test for the dilation order based on cumulative residual Tsallis entropy of order α. The effect of the values of parameter α on the power of the test statistics is numerically investigated. The asymptotic distribution of the test statistic is given. The performance of the test statistic is evaluated using a simulation study. Finally, some numerical examples illustrating the theory are also given. [ABSTRACT FROM AUTHOR]

Using a minimum p-value principle, a new two-sample test MIN3 is proposed in the paper. The cumulative distribution function of the MIN3 test statistic is studied and approximated by the Beta distribution of the third kind. Lower percentage points of the distribution of the new test statistic under the null hypothesis are computed. Also the test power for a lot of types of alternative hypotheses (with 0, 1 and 2 point(-s) of the intersection(-s) of survival functions) is studied and we found that the usage of the MIN3 test is a preferred strategy by the Wald and Savage decision-making criteria under risk and uncertainty. The results of application of the MIN3 test are shown for two examples from lifetime data analysis. [ABSTRACT FROM AUTHOR]

In the present paper, we use the already defined alpha-divergence and gamma-divergence for constructing some goodness of fit tests for exponentiality. These divergence measures are very robust with respect to outliers. Since the existence of outliers among statistical data can be lead to misleading results, therefore utilizing these divergence measures can be of importance. In order to construct test statistics, two estimators are used for alpha-divergence and gamma-divergence. In the first one, we consider the alpha-divergence and gamma-divergence of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF) and is proposed as an EDF-based goodness of fit test statistic. The second one is an estimator in manner of Vasicek entropy estimator. Simulation results indicate that in comparison with the other tests statistics, our mentioned test statistics almost in most of the cases have higher power. Finally, two examples containing outliers illustrate the importance and use of the proposed tests. [ABSTRACT FROM AUTHOR]

The excess switching activity during testing increases the power dissipation beyond the normal operation of the circuit. The non-linear power distribution creates localized heating called hotspot which results in the structural damage and increased cooling package cost. The temperature of a particular block depends on heat generation and dissipation of the circuit blocks. The uniformity in power distribution among the circuit blocks is the key requirement for temperature reduction. The unspecified bits present in the test patterns are utilized to reduce the switching activity during testing. In this paper, we present an event-driven based power analysis and temperature aware Xfilling to reduce the total power dissipation among the circuit blocks in such a way to reduce peak temperature. To reduce the peak temperature, the power dissipation of each block is monitored with the help of fillings the X-bits. The experiments are carried out with the ISCAS'89 benchmark circuit and show a significant reduction in peak temperature and ensure uniform power distribution during testing. [ABSTRACT FROM AUTHOR]

We provide a nonparametric revealed preference approach to demand analysis based on homothetic efficiency. Homotheticity is widely assumed (often implicitly) because it is a convenient and often useful restriction. However, this assumption is rarely tested, and data rarely satisfy testable conditions. To overcome this, we provide a way to estimate homothetic efficiency of consumption choices. The method provides considerably higher discriminatory power against random behavior than the commonly used Afriat efficiency. We use experimental and household survey data to illustrate how our approach is useful for different empirical applications and can provide greater predictive success. [ABSTRACT FROM AUTHOR]

A methodology is proposed to compare the power of normality tests with a wide variety of alternative unimodal distributions. It is based on the representation of a distribution mosaic in which kurtosis varies vertically and skewness horizontally. The mosaic includes distributions such as exponential, Laplace or uniform, with normal occupying the centre. Simulation is used to determine the probability of a sample from each distribution in the mosaic being accepted as normal. We demonstrate our proposal by applying it to the analysis and comparison of some of the most well-known tests. [ABSTRACT FROM AUTHOR]