BAYESIAN DEMONSTRATION TEST METHOD WITH MIXED BETA DISTRIBUTION

A complex mechatronics system Bayesian plan of demonstration test is studied based on the mixed beta distribution. During product design and improvement various information is appropriately considered by introducing inheritance factor, moreover, the inheritance factor is thought as a random variable, and the Bayesian decision of the qualification test plan is obtained, and the correctness of a Bayesian model presented is verified. The results show that the quantity of the test is too conservative according to classical methods under small binomial samples. Although traditional Bayesian analysis can consider test information of related or similar products, it ignores differences between such products. The method has solved the above problem, furthermore, considering the requirement in many practical projects, the differences among this method, the classical method and Bayesian with beta distribution are compared according to the plan of reliability acceptance test.

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

Parameters Estimation of a Bivariate Generalized Poisson Distribution with Applications to Metabolic Syndrome Data

Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.

Research on magnetic testing method of stress distribution

For implementing nondestructive evaluation of stress distribution inside ferromagnetic material, a magnetic testing method was developed which does not need artificial magnetizing field. This method was implemented by testing the normal component of the magnetic flux leakage above the object being tested with a constant lift off from 1 to 10?mm. The distribution of the stress inside the specimen can be gotten from that of the normal component of the magnetic flux leakage. A stress concentration specimen, which is a 10?mm thickness mild steel plate with a welding seam on it, was tested using this method. The stress distribution of the magnetic testing was identical with that of small hole stress testing method. It indicates that the stress distribution of ferromagnetic material can be known by the magnetic testing method.

AFFECTION OF SIZE-DISTRIBUTION TESTING APPARATUS ON DETERMINED RESULTS

This paper comprehensively analyzes every factor affecting the medium sedimentating measurement of poivder size distribution, and based on this, selects the optimum condition. Three size testing apparatus are used for a-Al2O3 powder measurements and the measured results are analyzed and compared with each other by unary linear regression method.

High Moments Jarque-Bera Tests for Arbitrary Distribution Functions

The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.

Constant-Step Stress Accelerated Life Test of VFD under Logarithmic Normal Distribution Case

In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.

Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples

The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

Reply to 'Statistical testing and distribution for lead chloride toxicity'

We are very grateful for the letter written by Dr Lange,and indeed apologize for the mistakes noted in the word-ing of our text regarding statistical analysis.This wasdue to changes carried out while revising the manuscriptat the request of reviewers,whom we thank for,point-ing out several issues that were actually similar to thosenoted by Dr.Lange.Unfortunately,we were unable todescribe and discuss our findings properly in the context

The Permutation Test as an Ancillary Procedure for Comparing Zero-Inflated Continuous Distributions

Empirical estimates of power and Type I error can be misleading if a statistical test does not perform at the stated rejection level under the null hypothesis. We employed the permutation test to control the empirical type I errors for zero-inflated exponential distributions. The simulation results indicated that the permutation test can be used effectively to control the type I errors near the nominal level even the sample sizes are small based on four statistical tests. Our results attest to the permutation test being a valuable adjunct to the current statistical methods for comparing distributions with underlying zero-inflated data structures.

On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions

The main aim of the present paper is to study the robustness of the developed sequential probability ratio test (SPRT) for testing the hypothesis about scale parameter of gamma distribution with known shape parameter and exponential distribution with location parameter. The robustness of the SPRT for scale parameter of gamma distribution is studied when the shape parameter has undergone a change. The similar study is conducted for the scale parameter of exponential distribution when the location parameter has undergone a change. The expressions for operating characteristic and average sample number functions are derived. It is found in both the cases that the SPRT is robust only when there is a slight variation in the shape and location parameter in the respective distributions.

The Kolmogorov-Smirnov test for three redshift distributions of long gamma-ray bursts in the Swift Era

We investigate redshift distributions of three long burst samples, with the first sample containing 131 long bursts with observed redshifts, the second including 220 long bursts with pseudo-redshifts calculated by the variability-luminosity relation, and the third including 1194 long bursts with pseudo-redshifls calculated by the lag-luminosity relation, respectively. In the redshift range 0-1 the Kolmogorov-Smirnov probability of the observed redshift distribution and that of the variability-luminosity relation is large. In the redshift ranges 1-2, 2-3, 3-6.3 and 0-37, the Kolmogorov-Smirnov probabilities of the redshift distribution from lag-luminosity relation and the observed redshift distribution are also large. For the GRBs, which appear both in the two pseudo-redshift burst samples, the KS probability of the pseudo-redshift distribution from the lag-luminosity relation and the observed reshift distribution is 0.447, which is very large. Based on these results, some conclusions are drawn： i） the V-Liso relation might be more believable than the τ-Liso relation in low redshift ranges and the τ-Liso relation might be more real than the V-Liso relation in high redshift ranges; ii） if we do not consider the redshift ranges, the τ-Liso relation might be more physical and intrinsical than the V-Liso relation.

Inference for constant-stress accelerated life test with Type-I progressively hybrid censored data from Burr-XII distribution

This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.

A new two-part test based on density ratio model for zero-inflated continuous distributions

In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.

Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution

In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.

The Catch Distribution of Ommastrephes batramii in Squid Jigging Fishery and the Relationship between Fishing Ground and SST in the North Pacific Ocean in 2004

Neon flying squid Ommastrephes batramii is widely distributed in the North Pacific Ocean, which has become the main fishing species for Chinese squid jigging fleets since 1993. Many authors have made the studies on the fields of fishing ground and its environment conditions. However, the squid catch per fishing vessel attained the highest level of about 550 t in 2004. In this paper, the catch and its distribution in 2004 would be compared with the previous year. Based on the catch data from Chinese squid jigging vessels and sea surface temperature with the format of 1 °latitude by 1 °longitude from May to November in 2004, the distribution maps were drawn by Marine explorer 4.0. The results show that the production in the east waters to 160°E was low during May and July. During October and November, the production in the waters from 150°E to 160°E was relatively higher, which occupied 62.5 percent of the total catch. During November, the production in the west waters to 150°E was also low. The highest CPUE area located in the west waters to 150°E, the next was the area from 150°E to 160°E and the lowest CPUE area located in the east waters to 160°E. The SST in the fishing ground seems to change seasonally. The suitable SST for each month is as follows： 12-14 ℃ in May, 15 ℃ - 16 ℃ in June, 14 ℃ - 16 ℃ in July, 18 ℃ - 19 ℃ in August, 16 ℃ -17 ℃ in September, 15 ℃- 16 ℃ in October and 12 ℃ - 13 ℃ in November. The result of K-S test shows that the above monthly suitable SST is considered as the indicator of looking for the main fishing ground.

RESEARCH ON DISTRIBUTION PAIR OFBENT-AXIS PUMP

The oil film thickness of the distribution pair of the bent-axis pump is tested dynamically in this paper. On the basis of synthetical consideration of the leakage flow rate, the loss of power and the ability to resist contaminant of the distribution pair,the parameters used to describe the distribution state are optimized. According to theoretical analyses and experimental research, the structure of the distribution plate is improved, and the ability to resist contaminant wear of the distribution pair is increased. Thus, it is possible to prolong the service life and working reliability of the pump.