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Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribution. Tests are performed using goodness of fit measures between the edge multiplicity sequence of an observed multigraph, and the expected one according to a simple or composite hypothesis. Test statistics of Pearson type and of likelihood ratio type are used, and the expected values of the Pearson statistic under the different models are derived. Test performances based on simulations indicate that even for small number of edges, the null distributions of both statistics are well approximated by their asymptotic χ 2 -distribution. The non-null distributions of the test statistics can be well approximated by proposed adjusted χ 2 -distributions used for power approximations. The influence of RSM on both test statistics is substantial for small number of edges and implies a shift of their distributions towards smaller values compared to what holds true for the null distributions under IEA. Two applications on social networks are included to illustrate how the tests can guide in the analysis of social structure. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a new probability distribution named as inverse power Maxwell distribution. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in modeling upside-down lifetime data. Some statistical properties of this distribution are derived. In estimation viewpoint, five methods are used for estimating the unknown parameters of the distribution and these methods are performed through the simulation study. Finally, two real data sets were analyzed to illustrate the applicability of the proposed distribution, proving that it fits each real data set much better than some other existing distributions. [ABSTRACT FROM AUTHOR]

The logit binomial logistic dose response model is commonly used in applied research to model binary outcomes as a function of the dose or concentration of a substance. This model is easily tailored to assess the relative potency of two substances. Consequently, in instances where two such dose response curves are parallel so one substance can be viewed as a dilution of the other, the degree of that dilution is captured in the relative potency model parameter. It is incumbent that experimental researchers working in fields including biomedicine, environmental science, toxicology and applied sciences choose efficient experimental designs to run their studies to both fit their dose response curves and to garner important information regarding drug or substance potency. This article provides far-reaching practical design strategies for dose response model fitting and estimation of relative potency using key illustrations. These results are subsequently extended here to handle situations where the assessment of parallelism and the proper dose-scale are also of interest. Conclusions and recommended strategies are supported by both theoretical and simulation results. [ABSTRACT FROM AUTHOR]

In this article, we propose a robust statistical approach to select an appropriate error distribution, in a classical multiplicative heteroscedastic model. In a first step, unlike to the traditional approach, we do not use any GARCH-type estimation of the conditional variance. Instead, we propose to use a recently developed nonparametric procedure [31]: the local adaptive volatility estimation. The motivation for using this method is to avoid a possible model misspecification for the conditional variance. In a second step, we suggest a set of estimation and model selection procedures (Berk–Jones tests, kernel density-based selection, censored likelihood score, and coverage probability) based on the so-obtained residuals. These methods enable to assess the global fit of a set of distributions as well as to focus on their behaviour in the tails, giving us the capacity to map the strengths and weaknesses of the candidate distributions. A bootstrap procedure is provided to compute the rejection regions in this semiparametric context. Finally, we illustrate our methodology throughout a small simulation study and an application on three time series of daily returns (UBS stock returns, BOVESPA returns and EUR/USD exchange rates). [ABSTRACT FROM AUTHOR]

As the metropolitan city in Western China, Chengdu has been suffered from serious traffic congestion. The strategy of urban public transport priority was put into agenda to relieve traffic congestion. But the public transport sharing rate is only 27% in Chengdu which is much lower than the developed country. Consequently, it is of great importance to study the measures to improve the service, and provide technical support to the policy-makers. This paper selected the traffic corridor between Southwest Jiaotong University district and downtown as the experiment subject. The orthogonal design was used to generate stated preference questionnaires in order to achieve the reliable parameter estimates. Some variables were used to define the utility of the three alternatives and construct the Logit model. Then, the relationships between the cost, time variable and the choice probability of the public transport were analyzed. According to the results, we found that the orthogonal design does improve the goodness-of-fit. The workability of Multinomial Logit Model was better than Nest Logit model. We also put forward some effective measures to improve the service level of public transit, including reducing the access time to Metro, limiting parking supply to control the car use. [ABSTRACT FROM AUTHOR]

This paper investigates a new test for normality that is easy for biomedical researchers to understand and easy to implement in all dimensions. In terms of power comparison against a broad range of alternatives, the new test outperforms the best known competitors in the literature as demonstrated by simulation results. In addition, the proposed test is illustrated using data from real biomedical studies. [ABSTRACT FROM PUBLISHER]

Probability plots allow us to determine whether a set of sample observations is distributed according to a theoretical distribution. Plotting positions are fundamental elements in statistics and, in particular, for the construction of probability plots. In this paper, a new plotting position to construct different probability plots, such as Q–Q Plot, P–P Plot and S–P Plot, is proposed. The proposed definition is based on the median of theith order statistic of the theoretical distribution considered. The main feature of this plotting position formula is that it is independent of the theoretical distribution selected. Moreover, the procedure developed is ‘almost’ exact, reaching, without a high cost of time, an accuracy as great as we want, which avoids using approximations (proposed by other authors). [ABSTRACT FROM PUBLISHER]

This paper compares methods for modeling the probability of removal when variable amounts of removal effort are present. A hierarchical modeling framework can produce estimates of animal abundance and detection from replicated removal counts taken at different locations in a region of interest. A common method of specifying variation in detection probabilities across locations or replicates is with a logistic model that incorporates relevant detection covariates. As an alternative to this logistic model, we propose using a catch–effort (CE) model to account for heterogeneity in detection when a measure of removal effort is available for each removal count. This method models the probability of detection as a nonlinear function of removal effort and a removal probability parameter that can vary spatially. Simulation results demonstrate that the CE model can effectively estimate abundance and removal probabilities when average removal rates are large but both the CE and logistic models tend to produce biased estimates as average removal rates decrease. We also found that the CE model fits better than logistic models when estimating wild turkey abundance using harvest and hunter counts collected by the Minnesota Department of Natural Resources during the spring turkey hunting season. [ABSTRACT FROM AUTHOR]

This article presents a universal quantile-quantile (QQ) plot that may be used to assess the fit of a family of absolutely continuous distribution functions in a possibly non-homogeneous population. This plot is more general than probability plotting papers because it may be used for distributions having more than two parameters. It is also more general than standard quantile-quantile plots because it may be used for families of not-necessarily identical distributions. In particular, the universal QQ plot may be used in the context of non-homogeneous Poisson processes, generalized linear models, and other general models. [ABSTRACT FROM AUTHOR]

This paper discusses biplots of the between-set correlation matrix obtained by canonical correlation analysis. It is shown that these biplots can be enriched with the representation of the cases of the original data matrices. A representation of the cases that is optimal in the generalized least squares sense is obtained by the superposition of a scatterplot of the canonical variates on the biplot of the between-set correlation matrix. Goodness of fit statistics for all correlation and data matrices involved in canonical correlation analysis are discussed. It is shown that adequacy and redundancy coefficients are in fact statistics that express the goodness of fit of the original data matrices in the biplot. The within-set correlation matrix that is represented in standard coordinates always has a better goodness of fit than the within-set correlation matrix that is represented in principal coordinates. Given certain scalings, the scalar products between variable vectors approximate correlations better than the cosines of angles between variable vectors. Several data sets are used to illustrate the results. [ABSTRACT FROM AUTHOR]

The small-sample behaviour of power-divergence goodness-of-fit statistics with composite hypotheses was evaluated with multinomial models of up to five cells and up to three parameters. Their performance was assessed by comparing asymptotic test sizes with exact test sizes obtained by enumeration in the near right tail, where 1- ∈ (0.90, 0.95], and in the far right tail, where 1- ∈ (0.95, 0.99]. The study addressed all combinations of power-diparse JAS312HH01.sgmvergence estimates of indices ν ∈ {-1/2, 0, 1/3, 1/2, 2/3, 1, 3/ 2} and power-divergence statistics of indices λ ∈ {-1/2, 0, 1/3, 1/2, 2/3, 1, 3/2}. The results indicate that the asymptotic approximation is sufficiently accurate (by the criterion that the average exact size is no larger than ±10% of the nominal asymptotic test size) in the near right tail when ν=0 and λ=1/2, and in the far right tail when ν=0 and λ=1/3, in both cases providing that the smallest expectation in the composite hypothesis exceeds 5. The only exception to this rule is the case of models that render a near-equiprobable composite hypothesis on the boundaries of the parameter space, where average exact sizes are usually quite different from nominal sizes despite the fact that the smallest expectation in these conditions is usually well above 5. [ABSTRACT FROM AUTHOR]