Goodness–of–fit statistics and CMB data sets

AbstractMetric multidimensional scaling (MDS) is a widely used multivariate method with applications in almost all scientific disciplines. Eigenvalues obtained in the analysis are usually reported in order to calculate the over-all goodness-of-fit of the distance matrix. In this paper, we refine MDS goodness-of-fit calculations, proposing additional point and pairwise good-ness-of-fit statistics that can be used to filter poorly represented observations in MDS maps. The proposed statistics are especially relevant for large data sets that contain outliers, with typically many poorly fitted observations, and are helpful for improving MDS output and emphasising the most important features of the dataset. Several goodness-of-fit statistics are considered, and both Euclidean and non-Euclidean distance matrices are considered. Some examples with data from demographic, genetic and geographic studies are shown.

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The gamma exponentiated exponential-Weibull distribution

Filomat ◽

10.2298/fil1612159p ◽

2016 ◽

Vol 30 (12) ◽

pp. 3159-3170 ◽

Cited By ~ 5

Author(s):

Tibor Pogány ◽

Abdus Saboor

Keyword(s):

Biological Sciences ◽

Weibull Distribution ◽

Goodness Of Fit ◽

Data Sets ◽

Fit Statistics ◽

Positive Data ◽

Special Cases ◽

Likelihood Approach ◽

Anderson Darling ◽

Von Mises

Anewfour-parameter model called the gamma-exponentiated exponential-Weibull distribution is being introduced in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson-Darling and Cram?r-von Mises goodness-of-fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.

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An α-Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data

Mathematics ◽

10.3390/math9121400 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1400

Author(s):

Talha Arslan

Keyword(s):

Goodness Of Fit ◽

Rate Function ◽

Information Criteria ◽

Environmental Data ◽

Cumulative Distribution ◽

Data Sets ◽

Fit Statistics ◽

Bathtub Shape ◽

Comparison Results ◽

Environmental Events

Modeling environmental data plays a crucial role in explaining environmental phenomena. In some cases, well-known distributions, e.g., Weibull, inverse Weibull, and Gumbel distributions, cannot model environmental events adequately. Therefore, many authors tried to find new statistical distributions to represent environmental phenomena more accurately. In this paper, an α-monotone generalized log-Moyal (α-GlogM) distribution is introduced and some statistical properties such as cumulative distribution function, hazard rate function (hrf), scale-mixture representation, and moments are derived. The hrf of the α-GlogM distribution can form a variety of shapes including the bathtub shape. The α-GlogM distribution converges to generalized half-normal (GHN) and inverse GHN distributions. It reduces to slash GHN and α-monotone inverse GHN distributions for certain parameter settings. Environmental data sets are used to show implementations of the α-GlogM distribution and also to compare its modeling performance with its rivals. The comparisons are carried out using well-known information criteria and goodness-of-fit statistics. The comparison results show that the α-GlogM distribution is preferable over its rivals in terms of the modeling capability.

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Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽

10.3390/econometrics9010010 ◽

2021 ◽

Vol 9 (1) ◽

pp. 10

Author(s):

Šárka Hudecová ◽

Marie Hušková ◽

Simos G. Meintanis

Keyword(s):

Goodness Of Fit ◽

Probability Generating Function ◽

Parametric Bootstrap ◽

Real Data ◽

Data Sets ◽

Test Statistics ◽

Finite Sample ◽

Generalized Poisson ◽

Goodness Of Fit Tests ◽

Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

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Using Ultrasound and Inflammation to Improve Prediction of Ischemic Stroke: A Secondary Analysis of the Multi-Ethnic Study of Atherosclerosis

Cerebrovascular Diseases Extra ◽

10.1159/000514373 ◽

2021 ◽

pp. 37-43

Author(s):

Hediyeh Baradaran ◽

Alen Delic ◽

Ka-Ho Wong ◽

Nazanin Sheibani ◽

Matthew Alexander ◽

...

Keyword(s):

Ischemic Stroke ◽

Goodness Of Fit ◽

Primary Outcome ◽

Stroke Risk ◽

Secondary Analysis ◽

Predictor Variables ◽

Baseline Model ◽

Fit Statistics ◽

Ischemic Stroke Risk

Introduction: Current ischemic stroke risk prediction is primarily based on clinical factors, rather than imaging or laboratory markers. We examined the relationship between baseline ultrasound and inflammation measurements and subsequent primary ischemic stroke risk. Methods: In this secondary analysis of the Multi-Ethnic Study of Atherosclerosis (MESA), the primary outcome is the incident ischemic stroke during follow-up. The predictor variables are 9 carotid ultrasound-derived measurements and 6 serum inflammation measurements from the baseline study visit. We fit Cox regression models to the outcome of ischemic stroke. The baseline model included patient age, hypertension, diabetes, total cholesterol, smoking, and systolic blood pressure. Goodness-of-fit statistics were assessed to compare the baseline model to a model with ultrasound and inflammation predictor variables that remained significant when added to the baseline model. Results: We included 5,918 participants. The primary outcome of ischemic stroke was seen in 105 patients with a mean follow-up time of 7.7 years. In the Cox models, we found that carotid distensibility (CD), carotid stenosis (CS), and serum interleukin-6 (IL-6) were associated with incident stroke. Adding tertiles of CD, IL-6, and categories of CS to a baseline model that included traditional clinical vascular risk factors resulted in a better model fit than traditional risk factors alone as indicated by goodness-of-fit statistics. Conclusions: In a multiethnic cohort of patients without cerebrovascular disease at baseline, we found that CD, CS, and IL-6 helped predict the occurrence of primary ischemic stroke. Future research could evaluate if these basic ultrasound and serum measurements have implications for primary prevention efforts or clinical trial inclusion criteria.

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A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

Engineering Proceedings ◽

10.3390/engproc2021005010 ◽

2021 ◽

Vol 5 (1) ◽

pp. 10

Author(s):

Mark Levene

Keyword(s):

Time Series ◽

Goodness Of Fit ◽

Marginal Distribution ◽

Hypothesis Test ◽

Data Sets ◽

Test Statistic ◽

Sample Test ◽

Kolmogorov Smirnov ◽

Heavy Tailed ◽

Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

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An Improved Approach for Reduction of Defect Density Using Optimal Module Sizes

Advances in Software Engineering ◽

10.1155/2014/803530 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

Dinesh Verma ◽

Shishir Kumar

Keyword(s):

Goodness Of Fit ◽

Defect Density ◽

Optimal Size ◽

Data Sets ◽

Density Parameter ◽

Proposed Model ◽

Module Size ◽

Curve Fitting Method ◽

Improved Model ◽

Effective Distribution

Nowadays, software developers are facing challenges in minimizing the number of defects during the software development. Using defect density parameter, developers can identify the possibilities of improvements in the product. Since the total number of defects depends on module size, so there is need to calculate the optimal size of the module to minimize the defect density. In this paper, an improved model has been formulated that indicates the relationship between defect density and variable size of modules. This relationship could be used for optimization of overall defect density using an effective distribution of modules sizes. Three available data sets related to concern aspect have been examined with the proposed model by taking the distinct values of variables and parameter by putting some constraint on parameters. Curve fitting method has been used to obtain the size of module with minimum defect density. Goodness of fit measures has been performed to validate the proposed model for data sets. The defect density can be optimized by effective distribution of size of modules. The larger modules can be broken into smaller modules and smaller modules can be merged to minimize the overall defect density.

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Quantifying paleogeography using biogeography: a test case for the Ordovician and Silurian of Avalonia based on brachiopods and trilobites

Paleobiology ◽

10.1666/0094-8373(2002)028<0343:qpubat>2.0.co;2 ◽

2002 ◽

Vol 28 (3) ◽

pp. 343-363 ◽

Cited By ~ 33

Author(s):

David C. Lees ◽

Richard A. Fortey ◽

L. Robin M. Cocks

Keyword(s):

Goodness Of Fit ◽

Total Evidence ◽

Pairwise Distance ◽

Test Case ◽

Data Sets ◽

Plate Tectonic ◽

Plate Model ◽

Optimal Arrangement ◽

Evidence Analysis ◽

Better Than

Despite substantial advances in plate tectonic modeling in the last three decades, the postulated position of terranes in the Paleozoic has seldom been validated by faunal data. Fewer studies still have attempted a quantitative approach to distance based on explicit data sets. As a test case, we examine the position of Avalonia in the Ordovician (Arenig, Llanvirn, early Caradoc, and Ashgill) to mid-Silurian (Wenlock) with respect to Laurentia, Baltica, and West Gondwana. Using synoptic lists of 623 trilobite genera and 622 brachiopod genera for these four plates, summarized as Venn diagrams, we have devised proportional indices of mean endemism (ME, normalized by individual plate faunas to eliminate area biogeographic effects) and complementarity (C) for objective paleobiogeographic comparisons. These can discriminate the relative position of Avalonia by assessing the optimal arrangement of inter-centroid distances (measured as great circles) between relevant pairs of continental masses. The proportional indices are used to estimate the “goodness-of-fit” of the faunal data to two widely used dynamic plate tectonic models for these time slices, those of Smith and Rush (1998) and Ross and Scotese (1997). Our faunal data are more consistent with the latter model, which we use to suggest relationships between faunal indices for the five time slices and new rescaled inter-centroid distances between all six plate pairs. We have examined linear and exponential models in relation to continental separation for these indices. For our generic data, the linear model fits distinctly better overall. The fits of indices generated by using independent trilobite and brachiopod lists are mostly similar to each other at each time slice and for a given plate, reflecting a common biogeographic signal; however, the indices vary across the time slices. Combining groups into the same matrix in a “total evidence” analysis performs better still as a measure of distance for mean endemism in the “Scotese” plate model. Four-plate mean endemism performs much better than complementarity as an indicator of pairwise distance for either plate model in the test case.

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Two-Parameter Nwikpe (TPAN) Distribution with Application

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v12i130279 ◽

2021 ◽

pp. 56-67

Author(s):

Barinaadaa John Nwikpe ◽

Isaac Didi Essi

Keyword(s):

Goodness Of Fit ◽

Continuous Distribution ◽

Real Life ◽

Moment Generating Function ◽

Statistical Properties ◽

Likelihood Method ◽

Data Sets ◽

Method Of Moment ◽

Two Parameter ◽

New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established. The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

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Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v14i230325 ◽

2021 ◽

pp. 41-59

Author(s):

Hussein Ahmad Abdulsalam ◽

Sule Omeiza Bashiru ◽

Alhaji Modu Isa ◽

Yunusa Adavi Ojirobe

Keyword(s):

Goodness Of Fit ◽

Negative Binomial ◽

Likelihood Estimation ◽

Statistical Properties ◽

Rainfall Data ◽

Parameter Estimates ◽

Data Sets ◽

Unknown Parameters ◽

Exponentiated Weibull ◽

Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

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