Stats

15 pages, 369 KiB

Open AccessArticle

Statistical Inference for Progressive Stress Accelerated Life Testing with Birnbaum-Saunders Distribution

by Naijun Sha

Stats 2018, 1(1), 189-203; https://doi.org/10.3390/stats1010014 - 12 Dec 2018

Cited by 7 | Viewed by 2017

As a result of the two-parameter Birnbaum–Saunders (BS) distribution being successful in modelling fatigue failure times, several extensions of this model have been explored from different aspects. In this article, we consider a progressive stress accelerated life testing for the BS model to [...] Read more.

As a result of the two-parameter Birnbaum–Saunders (BS) distribution being successful in modelling fatigue failure times, several extensions of this model have been explored from different aspects. In this article, we consider a progressive stress accelerated life testing for the BS model to introduce a generalized Birnbaum–Saunders (we call it Type-II GBS) distribution on the lifetime of products in the test. We outline some interesting properties of this highly flexible distribution, present the Fisher’s information in the maximum likelihood estimation method, and propose a new Bayesian approach for inference. Simulation studies are carried out to assess the performance of the methods under various settings of parameter values and sample sizes. Real data are analyzed for illustrative purposes to demonstrate the efficiency and accuracy of the proposed Bayesian method over the likelihood-based procedure. Full article

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13 pages, 323 KiB

Open AccessArticle

A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution

by Durga H. Kutal and Lianfen Qian

Stats 2018, 1(1), 176-188; https://doi.org/10.3390/stats1010013 - 15 Nov 2018

Cited by 6 | Viewed by 3657

Abstract

This paper considers a non-mixture cure model for right-censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Compared with [...] Read more.

This paper considers a non-mixture cure model for right-censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Compared with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data. Full article

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7 pages, 211 KiB

Open AccessArticle

Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles

by Stan Lipovetsky and Michael Conklin

Stats 2018, 1(1), 169-175; https://doi.org/10.3390/stats1010012 - 14 Nov 2018

Cited by 8 | Viewed by 2621

Abstract

A description of Likert scales can be given using the multipoles technique known in quantum physics and applied to behavioral sciences data. This paper considers decomposition of Likert scales by the multipoles for the application of decreasing the respondents’ heterogeneity. Due to cultural [...] Read more.

A description of Likert scales can be given using the multipoles technique known in quantum physics and applied to behavioral sciences data. This paper considers decomposition of Likert scales by the multipoles for the application of decreasing the respondents’ heterogeneity. Due to cultural and language differences, different respondents habitually use the lower end, the mid-scale, or the upper end of the Likert scales which can lead to distortion and inconsistency in data across respondents. A big impact of different kinds of respondent is well known, for instance, in international studies, and it is called the problem of high and low raters. Application of a multipoles technique to the row-data smoothing via prediction of individual rates by the histogram of the Likert scale tiers produces better results than standard row-centering in data. A numerical example by marketing research data shows that the results are encouraging: while a standard row-centering produces a poor outcome, the dipole-adjustment noticeably improves the obtained segmentation results. Full article

14 pages, 2716 KiB

Open AccessArticle

A New Signal Processing Approach for Discrimination of EEG Recordings

by Hossein Hassani, Mohammad Reza Yeganegi and Emmanuel Sirimal Silva

Stats 2018, 1(1), 155-168; https://doi.org/10.3390/stats1010011 - 08 Nov 2018

Cited by 6 | Viewed by 2619

Abstract

Classifying brain activities based on electroencephalogram (EEG) signals is one of the important applications of time series discriminant analysis for diagnosing brain disorders. In this paper, we introduce a new method based on the Singular Spectrum Analysis (SSA) technique for classifying brain activity [...] Read more.

Classifying brain activities based on electroencephalogram (EEG) signals is one of the important applications of time series discriminant analysis for diagnosing brain disorders. In this paper, we introduce a new method based on the Singular Spectrum Analysis (SSA) technique for classifying brain activity based on EEG signals via an application into a benchmark dataset for epileptic study with five categories, consisting of 100 EEG recordings per category. The results from the SSA based approach are compared with those from discrete wavelet transform before proposing a hybrid SSA and principal component analysis based approach for improving accuracy levels further. Full article

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21 pages, 731 KiB

Open AccessArticle

Causality between Oil Prices and Tourist Arrivals

by Xu Huang, Emmanuel Silva and Hossein Hassani

Stats 2018, 1(1), 134-154; https://doi.org/10.3390/stats1010010 - 20 Oct 2018

Cited by 4 | Viewed by 3393

Abstract

This paper investigates the causal relationship between oil price and tourist arrivals to further explain the impact of oil price volatility on tourism-related economic activities. The analysis itself considers the time domain, frequency domain, and information theory domain perspectives. Data relating to the [...] Read more.

This paper investigates the causal relationship between oil price and tourist arrivals to further explain the impact of oil price volatility on tourism-related economic activities. The analysis itself considers the time domain, frequency domain, and information theory domain perspectives. Data relating to the US and nine European countries are exploited in this paper with causality tests which include the time domain, frequency domain, and Convergent Cross Mapping (CCM). The CCM approach is nonparametric and therefore not restricted by assumptions. We contribute to existing research through the successful and introductory application of an advanced method and via the uncovering of significant causal links from oil prices to tourist arrivals. Full article

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22 pages, 3741 KiB

Open AccessArticle

Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application

by Elżbieta Antczak

Stats 2018, 1(1), 112-133; https://doi.org/10.3390/stats1010009 - 29 Sep 2018

Cited by 8 | Viewed by 2800

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 [...] Read more.

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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14 pages, 247 KiB

Open AccessReview

Recent Extensions to the Cochran–Mantel–Haenszel Tests

by J. C. W. Rayner and Paul Rippon

Stats 2018, 1(1), 98-111; https://doi.org/10.3390/stats1010008 - 26 Sep 2018

Cited by 5 | Viewed by 3818

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 [...] Read more.

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

6 pages, 231 KiB

Open AccessArticle

Smooth Tests of Fit for the Lindley Distribution

by D. J. Best and J. C. W. Rayner

Stats 2018, 1(1), 92-97; https://doi.org/10.3390/stats1010007 - 22 Jul 2018

Cited by 2 | Viewed by 2239

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 [...] Read more.

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

15 pages, 518 KiB

Open AccessArticle

A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications

by Broderick O. Oluyede, Boikanyo Makubate, Adeniyi F. Fagbamigbe and Precious Mdlongwa

Stats 2018, 1(1), 77-91; https://doi.org/10.3390/stats1010006 - 09 Jun 2018

Cited by 6 | Viewed by 3006

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 [...] Read more.

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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29 pages, 599 KiB

Open AccessArticle

The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

by Freddy Hernández and Viviana Giampaoli

Stats 2018, 1(1), 48-76; https://doi.org/10.3390/stats1010005 - 31 May 2018

Cited by 3 | Viewed by 3381

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 [...] Read more.

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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16 pages, 910 KiB

Open AccessArticle

A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications

by Gauss Moutinho Cordeiro, Maria Do Carmo Soares De Lima, Edwin Moisés Marcos Ortega and Adriano Kamimura Suzuki

Stats 2018, 1(1), 32-47; https://doi.org/10.3390/stats1010004 - 18 May 2018

Cited by 2 | Viewed by 2878

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 [...] Read more.

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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11 pages, 2508 KiB

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

by Ashuin Kammar, María Elena Hernández-Hernández, Patricia López-Moreno, Angélica María Ortíz-Bueno and María De Lurdez Consuelo Martínez-Montaño

Stats 2018, 1(1), 21-31; https://doi.org/10.3390/stats1010003 - 16 May 2018

Cited by 1 | Viewed by 3175

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. [...] Read more.

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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7 pages, 287 KiB

Open AccessArticle

On Moments of Gamma—Exponentiated Functional Distribution

by Katarzyna Górska, Andrzej Horzela and Tibor K. Pogány

Stats 2018, 1(1), 14-20; https://doi.org/10.3390/stats1010002 - 30 Mar 2018

Viewed by 2549

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 [...] Read more.

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

13 pages, 291 KiB

Open AccessFeature PaperArticle

A Nonparametric Statistical Approach to Content Analysis of Items

by Diego Marcondes and Nilton Rogerio Marcondes

Stats 2018, 1(1), 1-13; https://doi.org/10.3390/stats1010001 - 01 Feb 2018

Cited by 2 | Viewed by 3250

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 [...] Read more.

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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Stats, Volume 1, Issue 1 (December 2018) – 14 articles

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