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Stats, Volume 1, Issue 1 (December 2018)

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Open AccessArticle Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application
Stats 2018, 1(1), 112-133; https://doi.org/10.3390/stats1010009
Received: 30 July 2018 / Revised: 23 September 2018 / Accepted: 26 September 2018 / Published: 29 September 2018
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Abstract
This paper investigates how to determine the values (elements) of spatial weights in a spatial matrix (W) endogenously from the data. To achieve this goal, geostatistical tools (standard deviation ellipsis, semivariograms, semivariogram clouds, and surface trend models) were used. Then, in
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This paper investigates how to determine the values (elements) of spatial weights in a spatial matrix (W) endogenously from the data. To achieve this goal, geostatistical tools (standard deviation ellipsis, semivariograms, semivariogram clouds, and surface trend models) were used. Then, in the econometric part of the analysis, the effect of applying different variants of matrices was examined. The study was conducted on a sample of 279 Polish towns from 2005–2015. Variables were related to the quantity of produced waste and economic development. Both exploratory spatial data analysis and estimations of spatial panel and seemingly unrelated regression models were performed by including particular W matrices in the study (exogenous-random as well as distance and directional matrices constructed based on data). The results indicated that (1) geostatistical tools can be effectively used to build Ws; (2) outcomes of applying different matrices did not exclude but supplemented one another, although the differences were significant; (3) the most precise picture of spatial dependence was achieved by including distance matrices; and (4) the values of the assessed parameter at the regressors did not significantly change, although there was a change in the strength of the spatial dependency. Full article
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Open AccessReview Recent Extensions to the Cochran–Mantel–Haenszel Tests
Stats 2018, 1(1), 98-111; https://doi.org/10.3390/stats1010008
Received: 28 June 2018 / Revised: 19 September 2018 / Accepted: 19 September 2018 / Published: 26 September 2018
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Abstract
The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data. The inference is conditional on the treatment and outcome totals on each stratum being known before sighting the data. The CMH tests are important for analysing randomised
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The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data. The inference is conditional on the treatment and outcome totals on each stratum being known before sighting the data. The CMH tests are important for analysing randomised blocks data when the responses are categorical rather than continuous. This overview of some recent extensions to CMH testing first describes the traditional CMH tests and then explores new alternative presentations of the ordinal CMH tests. Next, the ordinal CMH tests will be extended so they can be used to test for higher moment effects. Finally, unconditional analogues of the extended CMH tests will be developed. Full article
Open AccessArticle Smooth Tests of Fit for the Lindley Distribution
Stats 2018, 1(1), 92-97; https://doi.org/10.3390/stats1010007
Received: 14 June 2018 / Revised: 13 July 2018 / Accepted: 13 July 2018 / Published: 22 July 2018
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Abstract
We consider the little-known one parameter Lindley distribution. This distribution may be of interest as it appears to be more flexible than the exponential distribution, the Lindley fitting more data than the exponential. We give smooth tests of fit for this distribution. The
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We consider the little-known one parameter Lindley distribution. This distribution may be of interest as it appears to be more flexible than the exponential distribution, the Lindley fitting more data than the exponential. We give smooth tests of fit for this distribution. The smooth test for the Lindley has power comparable with the Anderson-Darling test. Advantages of the smooth test are discussed. Examples that illustrate the flexibility of this distributions is given. Full article
Open AccessArticle A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications
Stats 2018, 1(1), 77-91; https://doi.org/10.3390/stats1010006
Received: 28 March 2018 / Revised: 30 May 2018 / Accepted: 1 June 2018 / Published: 9 June 2018
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Abstract
A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic
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A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution. Full article
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Open AccessArticle The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model
Stats 2018, 1(1), 48-76; https://doi.org/10.3390/stats1010005
Received: 17 March 2018 / Revised: 25 May 2018 / Accepted: 29 May 2018 / Published: 31 May 2018
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Abstract
Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of
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Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification. Full article
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Open AccessArticle A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications
Stats 2018, 1(1), 32-47; https://doi.org/10.3390/stats1010004
Received: 19 March 2018 / Revised: 24 April 2018 / Accepted: 14 May 2018 / Published: 18 May 2018
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Abstract
We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on
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We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum–Saunders–Poisson random variable. For censored data, we estimate the parameters of the regression model using maximum likelihood. We investigate the accuracy of the maximum likelihood estimates using Monte Carlo simulations. The importance of the proposed models, when compared to existing models, is illustrated by means of two real data sets. Full article
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Open AccessArticle Probability and Body Composition of Metabolic Syndrome in Young Adults: Use of the Bayes Theorem as Diagnostic Evidence of the Waist-to-Height Ratio
Stats 2018, 1(1), 21-31; https://doi.org/10.3390/stats1010003
Received: 17 April 2018 / Revised: 8 May 2018 / Accepted: 15 May 2018 / Published: 16 May 2018
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Abstract
Metabolic syndrome (MS) directly increases the risk of cardiovascular diseases. Childhood and adulthood have been the most studied in MS, leaving aside the young adult population. This study aimed to compare the epidemiological probabilities between MS and different anthropometric parameters of body composition.
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Metabolic syndrome (MS) directly increases the risk of cardiovascular diseases. Childhood and adulthood have been the most studied in MS, leaving aside the young adult population. This study aimed to compare the epidemiological probabilities between MS and different anthropometric parameters of body composition. Using a cross-sectional study with the sample of 1351 young adults, different body composition parameters were obtained such as Waist Circumference (WC), Body Mass Index (BMI), Body Fat% (BF%), Waist-to-Height Ratio (WHtR), and Waist-Hip Ratio. The Bayes Theorem was applied to estimate the conditional probability that any subject developed MS with an altered anthropometric parameter of body composition. Areas under receiver operating characteristic curves (AUCs) and adjusted odds ratios of the five parameters were analyzed in their optimal cutoffs. The conditional probability of developing MS with an altered anthropometric parameter was 17% in WHtR, WC, and Waist-hip R. Furthermore, body composition parameters were adjusted by age, BMI, and gender. Only WHtR (OR = 9.43, CI = 3.4–26.13, p < 0.0001), and BF% (OR = 3.18, CI = 1.42–7.13, p = 0.005) were significant, and the sensitivity (84%) and the AUCs (86%) was higher in WHtR than other parameters. In young adults, the WHtR was the best predictor of metabolic syndrome. Full article
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Open AccessArticle On Moments of Gamma—Exponentiated Functional Distribution
Stats 2018, 1(1), 14-20; https://doi.org/10.3390/stats1010002
Received: 24 February 2018 / Revised: 25 March 2018 / Accepted: 27 March 2018 / Published: 30 March 2018
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Abstract
In this note we discuss the development of a new Gamma exponentiated functional GE(α,h) distribution, using the Gamma baseline distribution generating method by Zografos and Balakrishnan. The raw moments of the Gamma exponentiated functional GE(α,
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In this note we discuss the development of a new Gamma exponentiated functional GE ( α , h ) distribution, using the Gamma baseline distribution generating method by Zografos and Balakrishnan. The raw moments of the Gamma exponentiated functional GE ( α , h ) distribution are derived. The related probability distribution class is characterized in terms of Lambert W-function. Full article
Open AccessFeature PaperArticle A Nonparametric Statistical Approach to Content Analysis of Items
Stats 2018, 1(1), 1-13; https://doi.org/10.3390/stats1010001
Received: 6 December 2017 / Revised: 23 January 2018 / Accepted: 25 January 2018 / Published: 1 February 2018
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Abstract
In order to use psychometric instruments to assess a multidimensional construct, we may decompose it into dimensions and, in order to assess each dimension, develop a set of items, so one may assess the construct as a whole, by assessing its dimensions. In
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In order to use psychometric instruments to assess a multidimensional construct, we may decompose it into dimensions and, in order to assess each dimension, develop a set of items, so one may assess the construct as a whole, by assessing its dimensions. In this scenario, content analysis of items aims to verify if the developed items are assessing the dimension they are supposed to by requesting the judgement of specialists in the studied construct about the dimension that the developed items assess. This paper aims to develop a nonparametric statistical approach based on the Cochran’s Q test to analyse the content of items in order to present a practical method to assess the consistency of the content analysis process; this is achieved by the development of a statistical test that seeks to determine if all the specialists have the same capability to judge the items. A simulation study is conducted to check the consistency of the test and it is applied to a real validation process. Full article
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