Quadratic statistics for the goodness-of-fit test of the inverseGaussian distribution

The problem of using a quadratic test to examine the goodness-of-fit of an inverse Gaussian distribution with unknown parameters is discussed. Tables of approximate critical values of Anderson-Darling, Cramer-von Mises, and Watson test statistics are presented in a format requiring only the sample size and the estimated value of the shape parameter. A relationship is found between the sample size and critical values of these test statistics, thus eliminating a need to interpolate among sample sizes given in the table. A power study showed that the proposed modified goodness-of-fit procedures have reasonably good power     

Goodness-of-fit tests based on spacings for progressively type-II censored data from a general location-scale distribution

There has been extensive research on goodness-of-fit procedures for testing whether or not a sample comes from a specified distribution. These goodness-of-fit tests range from graphical techniques, to tests which exploit characterization results for the specified underlying model. In this article, we propose a goodness-of-fit test for the location-scale family based on progressively Type-II censored data. The test statistic is based on sample spacings, and generalizes a test procedure proposed by Tiku . The distribution of the test statistic is shown to be approximated closely by a s-normal distribution. However, in certain situations it would be better to use simulated critical values instead of the s-normal approximation. We examine the performance of this test for the s-normal and extreme-value (Gumbel) models against different alternatives through Monte Carlo simulations. We also discuss two methods of power approximation based on s-normality, and compare the results with those obtained by simulation. Results of the simulation study for a wide range of sample sizes, censoring schemes, and different alternatives reveal that the proposed test has good power properties in detecting departures from the s-normal and Gumbel distributions. Finally, we illustrate the method proposed here using real data from a life-testing experiment. It is important to mention here that this test can be extended to multi-sample situations in a manner similar to that of Balakrishnan et al.     

Goodness-of-Fit Test for Extreme-Value Distribution

A test of fit for the extreme-value distribution with unknown parameters is adapted from the work of Vasicek. This test, based on sample entropy, has desirable power compared with analogues of some nonparametric tests and the Mann test. The test statistic is easily calculated by use of the coefficient tables for the MVLUE.     

On a t-Test for the Scale Parameter Based on Sample Percentiles

A Student's test of Ho:? = ?o against ? ? ?o of the scale parameter ? of the Normal, logistic, and Cauchys distributions, when the location parameter ? is known is based on a few sample percentiles selected from a large sample. Tables facilitating the computation of the test statistic are provided. The significance level and power of the test statistic for sample sizes ? 200 are simulated by the Monte Carlo method and compared with the significance level and power when it is assumed to have its asymptotic distribution.     

Relative efficiency of the sequential probability ratio test in signal detection

The relative efficiency of a sequential hypothesis test compared to a fixed sample size test is defined as the ratio of the expected sample size of the sequential test to the sample size of the fixed sample size test with the same size and power. Asymptotic behavior of the relative efficiency is studied for the detection of a constant signal in additive noise. With some regularity conditions imposed on the noise density, the asymptotic relative efficiency of the sequential probability ratio test with respect to the corresponding fixed sample size likelihood ratio test is a function of the size and the power. As the size a approaches zero and the power approaches unity, this asymptotic relative efficiency has a limiting value depending on the functional relationship of a and1 - betaas they approach zero. Comparison of the power functions is also studied.     

Sparsity adaptive matching pursuit for face recognition

Sparse representation methods have exhibited promising performance for pattern recognition. However, these methods largely rely on the data sparsity available in advance and are usually sensitive to noise in the training samples. To solve these problems, this paper presents sparsity adaptive matching pursuit based sparse representation for face recognition (SAMPSR). This method adaptively explores the valid training samples that exactly represent the test via iterative updating. Next, the test samples are reconstructed via the valid training samples, and classification is performed subsequently. The two-phase strategy helps to improve the discriminating power of class probability distribution, and thus alleviates effect of the noise from the training samples to some extent and correctly performs classification. In addition, the method solves the sparse coefficient by comparing the residual between the test sample and the reconstructed sample instead of using the sparsity. A large number of experiments show that our method achieves promising performance.     

A Hybrid Decoupled Power Flow Method for Balanced Power Distribution Systems

This paper proposes a hybrid decoupled power flow method for balanced power distribution systems with distributed generation sources.The method formulates the power flow equations in active power and reactive power decoupled form with polar coordinates.Second-order terms are included in the active power mismatch iteration,and constant Jacobian and Hessian matrices are used.A hybrid direct and indirect solution technique is used to achieve efficiency and robustness of the algorithm.Active power correction is solved by means of a sparse lower triangular and upper triangular(LU) decomposition algorithm with partial pivoting,and the reactive power correction is solved by means of restarted generalized minimal residual algorithm with an incomplete LU pre-conditioner.Typical distribution generation models and distribution load models are included.The impact of zero-impedance branches is explicitly modeled through reconfiguring of the adjacent branches with impedances.Numerical examples on a sample distribution system with widespread photovoltaic installations are given to demonstrate the effectiveness of the proposed method.     

A test for the BMRL-t0 class

In this paper we propose a new non-parametric procedure to test the alternative hypothesis that a life distribution belongs to the class of better mean residual life at age t₀ (BMRL-t₀). Such a class is a proper subclass of NBUE class and contains the DMRL class. Our test is based on an L-statistic and its asymptotic normality is established to derive a large sample non-parametric test procedure. The asymptotic relative efficiencies of our test with respect to the existing tests are calculated to check on the power of the test. It is shown that the new test is quite comparable with other tests.     

Power?frequency distribution in a cavity containing a resonant ferrite sample

The letter investigates the distribution of power as a function of frequency in a cavity containing a resonant ferrite sample. Formulas and a Figure are presented for the maximum power that can be incident on the system without deterioration of the resonance linewidth of the sample.     

Nonuniform temperature and strain fields in a powered package

This paper analyzes the nonuniform temperature and strain fields resulting from power dissipation in an electronic package. A 208 lead plastic quad flat pack (PQFP) manufactured by Texas Instruments is used to show the temperature distribution and mechanical deformation resulting from power dissipation in the package. The package is tested experimentally and thermally modeled using finite element analysis to obtain the temperature distribution in the active package. The moire interferometry technique is used to acquire displacement contours of an active PQFP and the results are compared to a uniformly heated sample. The results revealed that the thermal loading due to internal power dissipation produces significantly different strains than a uniformly heated sample     

A Test of the Equality of Survival Distributions Based on Paired Observations from Conditionally Independent Exponential Distributions

A model describes the joint distribution of paired survival times based on certain reasonable assumptions appropriate for biological data generated in a clinical trial setting or for certain failure data. An exact parametric test for equality of mean survival times for data following this distribution is developed. The power of the exact test is investigated by a computer simulation study for various sample sizes and values of the model parameters and compared to that of alternative tests. Heretofore, researchers desiring to analyze paired survival data have resorted to paired t tests or nonparametric procedures such as the sign test or signed ranks test. The t-test is invalid for non-normally distributed data although the robustness of the test might minimize the difficulty. The nonparametric tests, by their nature, fail to use the data completely. This paper presents an exact parametric test based on a distribution whose justification requires rather modest and reasonable assumptions. Critical values for the test can be obtained from a table of the chi-square distribution. This exact test appears to be a viable alternative to non-parametric approaches to the analysis of paired survival data. It is extremely easy to calculate on a hand calculator. In fact, since no data storage is required (unlike the signed ranks test), the calculations can be readily programmed on a programmable calculator. The modeling of bivariate and multivariate survival data we believe has not been adequately addressed in the statistical and engineering literature. We hope that this paper will spark additional work.     

Goodness-of-fit tests based on Kullback-Leibler discriminationinformation

We present a general methodology for developing asymptotically distribution-free goodness-of-fit tests based on the Kullback-Leibler discrimination information. The tests are shown to be omnibus within an extremely large class of nonparametric global alternatives and to have good local power. The proposed test procedure is a nonparametric extension of the classical Neyman-Pearson log-likelihood ratio test and is based on mth-order spacings between order statistics cross-validated by the observed log likelihood. The developed method also generalizes Cox's procedure of testing separate families and covers virtually all parametric families of distributions encountered in statistics. It can also be viewed as a procedure based on sum-log functionals of nonparametric density-quantile estimators cross-validated by the log likelihood. With its good power properties, the method provides an extremely simple and potentially much better alternative to the classical empirical distribution function (EDF)-based test procedures. The important problem of selecting the order of spacings m in practice is also considered and a method based on maximizing the sample entropy constrained by the observed log likelihood is proposed. This data driven method of choosing m is demonstrated by Monte Carlo simulations to be more powerful than deterministic choices of m and thus provides a practically useful tool for implementing our test procedure     

Trend change in mean residual life

The authors consider a life distribution which shows a trend change in its mean residual life (MRL). The problem of testing such a trend change has been of great interest in reliability analysis. The authors propose a new procedure for testing the exponentiality against IDMRL or DMIRL, assuming that the proportion of the population, p, that dies at or before the change point of MRL is known. Their test provides a new competitor to the known test procedures, such as the Guess, Hollander, Proschan test and the Aly test. Based on the empirical powers of these tests against lognormal alternatives, their test outperforms the others for most sample sizes and most values of p and that all three tests achieve high power in detecting the trend change of MRL when p is very small and very large     

Accelerated life-tests for intermittent destructive inspection,with logistic failure-distribution

Statistically-optimal accelerated life-test plans are suggested for items whose lifetime follows a logistic distribution. Both the scale and location parameters of the lifetime distribution are functions of the stress level. The test plans accommodate intermittent destructive sampling. The number of sampled items which fail to pass the test at the time of each inspection follows a hypergeometric distribution; the number of defective items in the remaining sample which have not yet been tested follows a binomial distribution. Statistically-optimal designs provide test planners with a set of design inputs, such as: 2 stress-levels higher than use stress-level, a set of inspection times, sample allocation, and a censoring time that minimizes the asymptotic variance of the maximum likelihood estimator of a specified quantile of the lifetime distribution. However such a 2 stress-level optimal plan is not practical because model validation is rarely impossible with so few stress-levels at which to test. In order to overcome such impracticality compromise plans that require 3 stress-levels are also suggested at a fixed inspection interval-although these plans lose statistical efficiency     

A New Method for Goodness-of-Fit Testing Based on Type-II Right Censored Samples

We present a simple method for testing goodness-of-fit based on Type-II right censored samples. Applying the property of order statistics due to Malmquist, we can transform any conventional Type-II right censored sample of size $r$ out of $n$ from a uniform distribution to a complete sample of size $r$ from a uniform distribution. This result is used to develop the proposed goodness-of-fit test procedure. The simulation studies reveal that the proposed approach provides as good or better overall power than the method of Michael & Schucany.      

Goodness-of-fit tests for the power-law process

The power-law process is often used as a model for reliability growth of complex systems or reliability of repairable systems. Often goodness-of-fit tests are required to check the hypothesis that failure data came from a power-law process model. Three statistics, Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling, are considered for a goodness-of-fit test of a power-law process in the case of failure-truncated data. Tables of critical values for the three statistics are presented and the results of a power study are given under the alternative hypothesis that failure data came from a nonhomogeneous Poisson process with log-linear intensity function. This power comparison is a new result, which can guide in selecting a test statistic and sample size. The power study shows that the tests have acceptable power for some parameter values and the Cramer-von Mises statistic has the highest power for a sample-size ⩾20     

Spectral analysis of quantization noise in a single-loopsigma-delta modulator with DC input

An exact discrete-time analysis of the moments and spectra of the quantization noise of a discrete-time single-loop sigma-delta modulator with a DC input is presented. An exact difference equation for the discrete-time nonlinear system is used to evaluate the first- and second-order moments and power spectrum of the binary quantizer noise and the binary quantizer output for a single-loop sigma-delta encoder with a DC input. It is shown that the sample mean and power of the binary quantization noise are consistent with the common uniform distribution assumption, but that the autocorrelation and power spectrum are not consistent with the white noise assumption. The results are used to evaluate the overall sample average mean squared quantization error as a function of the decimation filter used     

雷达威力检测中替代等效推算方法研究

介绍了替代等效推算方法,讨论了替代等效推算方法在雷达检飞试验中的应用。以目标χ^2分布起伏统计模型来定义的五类典型的雷达目标,设计了雷达威力检测的模型,给出了雷达威力试验中不同飞行合作目标间替代等效推算关系,并对其应用进行了分析,为替代等效推算方法在靶场雷达检飞中的应用奠定了理论基础,在雷达检飞试验中具有一定的实际意义。     

Distinguishing between lognormal and Weibull distributions[time-to-failure data]

A previous method for deciding if a set of time-to-fail data follows a lognormal distribution or a Weibull distribution is expanded upon. Pearson's s-correlation coefficient is calculated for lognormal and Weibull probability plots of the time-to-fail data. The test statistic is the ratio of the two s-correlation coefficients. When "standardized", the lognormal and Weibull variables map into 1 of 2 gamma distributions with no dependence on the shape or scaling factors, confirming earlier observations. Using a set of Monte Carlo simulations, the test statistic was found to be s-normally distributed to good approximation. Formulas for estimating the mean and standard deviation of the test statistic were derived, allowing for an estimate of the probability of hypothesis test errors. As anticipated, the test capability increases with increasing sample size, but only if a substantial fraction of the parts actually fail. If less than 10% of the parts are stressed to failure, then it is almost impossible to distinguish between lognormal and Weibull distributions. If all parts are stressed to failure, the probability of making a correct choice is fair for sample sizes as small as 10, and becomes quite good if the sample size is at least 50. The statistical technique for distinguishing lognormal from Weibull distributions is presented. Its theoretical foundation is given at a qualitative level, and the range of useful application is explored. An approximate form for the distribution of the test statistic is inferred from Monte Carlo simulation     

Early reliability assessment by using deep censoring

A method is described for making direct characterizations of the early part of the intrinsic electromigration fail-time distribution of interconnects. The method involves stressing a large number of test lines only long enough for a relatively few lines to fail, enough to characterize the percentile of interest. Groups of test lines are electrically monitored to detect failures without having to measure individually the many lines on test. Two types of deep censoring (DC) are described: DC without removals (where more than one line failure in a group can be detected with confidence) and DC with removals (where, when one failure occurs, the other lines in the group are removed from the test). Sample estimates of sigma and of one or more early percentiles of the distribution are corrected for bias and their confidence limits calculated. DC offers important benefits over the present practice of placing tens of test lines on test to obtain sample estimates of t₅₀ and σ that are used to extrapolate to the early part of the log_e(fail-time) distribution. The benefits are reduced testing times, better confidence of the sample estimates of early percentages of the distribution, and the ability to detect extrinsic fail-time populations. A detailed procedure to implement the method is provided in the appendix.