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PloS One 2023Gul and Mohsin 2021 developed a new modified form of renowned "Half logistic" distribution introduced by Balakrishnan (1991) and named it half logistic-truncated...
Gul and Mohsin 2021 developed a new modified form of renowned "Half logistic" distribution introduced by Balakrishnan (1991) and named it half logistic-truncated exponential distribution (HL-TEXPD). Some mathematical characteristics are studied, including hazard function, Pth percentile, moment generating function and Shannon entropy. Simulation study is performed to examine the behaviour of parameter estimates. The proposed model is fitted on three real data sets to check its efficacy. Additionally, TTT (total time on test) plot is drawn to study the failure rate of the three data sets. The results verdict that HL-TEXPD can be efficiently utilized in the field of engineering and medical sciences based on the data sets under study contrary to the classical and baseline models.
Topics: Computer Simulation; Statistical Distributions; Entropy
PubMed: 37963157
DOI: 10.1371/journal.pone.0285992 -
PloS One 2016The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature,...
The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of segregation are implicitely tied to a single indicator, usually rely on an ambiguous definition of income classes, without any consensus on how to define neighbourhoods and to deal with the polycentric organization of large cities. In this paper, we address all these questions within a unique conceptual framework. We avoid the challenge of providing a direct definition of segregation and instead start from a definition of what segregation is not. This naturally leads to the measure of representation that is able to identify locations where categories are over- or underrepresented. From there, we provide a new measure of exposure that discriminates between situations where categories co-locate or repel one another. We then use this feature to provide an unambiguous, parameter-free method to find meaningful breaks in the income distribution, thus defining classes. Applied to the 2014 American Community Survey, we find 3 emerging classes-low, middle and higher income-out of the original 16 income categories. The higher-income households are proportionally more present in larger cities, while lower-income households are not, invalidating the idea of an increased social polarisation. Finally, using the density-and not the distance to a center which is meaningless in polycentric cities-we find that the richer class is overrepresented in high density zones, especially for larger cities. This suggests that density is a relevant factor for understanding the income structure of cities and might explain some of the differences observed between US and European cities.
Topics: Censuses; Cities; Ethnicity; Female; Humans; Income; Male; Population Density; Residence Characteristics; Social Segregation; Socioeconomic Factors; Statistical Distributions; Urban Population; White People
PubMed: 27315283
DOI: 10.1371/journal.pone.0157476 -
Biometrics Dec 2016The focus of this article is on the nature of the likelihood associated with N-mixture models for repeated count data. It is shown that the infinite sum embedded in the...
The focus of this article is on the nature of the likelihood associated with N-mixture models for repeated count data. It is shown that the infinite sum embedded in the likelihood associated with the Poisson mixing distribution can be expressed in terms of a hypergeometric function and, thence, in closed form. The resultant expression for the likelihood can be readily computed to a high degree of accuracy and is algebraically tractable. Specifically, the likelihood equations can be simplified to some advantage, the concentrated likelihood in the probability of detection formulated and problematic cases identified. The results are illustrated by means of a simulation study and a real world example. The study is extended to N-mixture models with a negative binomial mixing distribution and results similar to those for the Poisson case obtained. N-mixture models with mixing distributions which accommodate excess zeros and, separately, with a beta-binomial distribution rather than a binomial used to model the intra-site counts are also investigated. However the results for these settings, while computationally attractive, do not provide insight into the nature of the maximum likelihood estimates.
Topics: Animals; Biometry; Computer Simulation; Galliformes; Humans; Likelihood Functions; Models, Statistical; Poisson Distribution
PubMed: 27043770
DOI: 10.1111/biom.12521 -
PloS One 2018Fame and celebrity play an ever-increasing role in our culture. However, despite the cultural and economic importance of fame and its gradations, there exists no...
Fame and celebrity play an ever-increasing role in our culture. However, despite the cultural and economic importance of fame and its gradations, there exists no consensus method for quantifying the fame of an individual, or of comparing that of two individuals. We argue that, even if fame is difficult to measure with precision, one may develop useful metrics for fame that correlate well with intuition and that remain reasonably stable over time. Using datasets of recently deceased individuals who were highly renowned, we have evaluated several internet-based methods for quantifying fame. We find that some widely-used internet-derived metrics, such as search engine results, correlate poorly with human subject judgments of fame. However other metrics exist that agree well with human judgments and appear to offer workable, easily accessible measures of fame. Using such a metric we perform a preliminary investigation of the statistical distribution of fame, which has some of the power law character seen in other natural and social phenomena such as landslides and market crashes. In order to demonstrate how such findings can generate quantitative insight into celebrity culture, we assess some folk ideas regarding the frequency distribution and apparent clustering of celebrity deaths.
Topics: Famous Persons; Female; Humans; Internet; Judgment; Male; Probability; Statistical Distributions; Surveys and Questionnaires
PubMed: 29979792
DOI: 10.1371/journal.pone.0200196 -
BMC Bioinformatics Feb 2021The search for statistically significant relationships between molecular markers and outcomes is challenging when dealing with high-dimensional, noisy and collinear...
BACKGROUND
The search for statistically significant relationships between molecular markers and outcomes is challenging when dealing with high-dimensional, noisy and collinear multivariate omics data, such as metabolomic profiles. Permutation procedures allow for the estimation of adjusted significance levels without assuming independence among metabolomic variables. Nevertheless, the complex non-normal structure of metabolic profiles and outcomes may bias the permutation results leading to overly conservative threshold estimates i.e. lower than those from a Bonferroni or Sidak correction.
METHODS
Within a univariate permutation procedure we employ parametric simulation methods based on the multivariate (log-)Normal distribution to obtain adjusted significance levels which are consistent across different outcomes while effectively controlling the type I error rate. Next, we derive an alternative closed-form expression for the estimation of the number of non-redundant metabolic variates based on the spectral decomposition of their correlation matrix. The performance of the method is tested for different model parametrizations and across a wide range of correlation levels of the variates using synthetic and real data sets.
RESULTS
Both the permutation-based formulation and the more practical closed form expression are found to give an effective indication of the number of independent metabolic effects exhibited by the system, while guaranteeing that the derived adjusted threshold is stable across outcome measures with diverse properties.
Topics: Genetic Markers; Metabolome; Metabolomics; Models, Biological; Statistical Distributions
PubMed: 33579202
DOI: 10.1186/s12859-021-03975-2 -
Statistics in Medicine Jun 2019Regression to the mean (RTM) occurs when subjects having relatively high or low measurements are remeasured and found closer to the population mean. This phenomenon can...
Regression to the mean (RTM) occurs when subjects having relatively high or low measurements are remeasured and found closer to the population mean. This phenomenon can potentially lead to an inaccurate conclusion in a pre-post study design. Expressions are available for quantifying RTM when the distribution of pre and post observations are bivariate normal and bivariate Poisson. However, situations exist where the response variables are the number of successes in a fixed number of trials and follow the bivariate binomial distribution. In this article, expressions for quantifying RTM effects are derived when the underlying distribution is the bivariate binomial. Unlike the normal and Poisson distributions, the correlation between pre and post observations can be either negative or positive under the bivariate binomial distribution and the severity of RTM is greater in the former case. The percentage relative difference is used to highlight the differences in quantifying RTM under the bivariate binomial distribution and normal and Poisson approximations to the bivariate binomial distribution. Expressions for estimating RTM using the method of maximum likelihood along with its asymptotic distribution are derived. A simulation study is conducted to empirically assess the statistical properties of the RTM estimator and its asymptotic distribution. Data examples using the number of obese individuals and the number of nonconforming cardboard cans are discussed.
Topics: Adolescent; Age Factors; Binomial Distribution; Child; Child, Preschool; Computer Simulation; Efficiency, Organizational; Equipment Design; Female; Humans; Iowa; Male; Models, Statistical; Obesity; Poisson Distribution; Probability; Research Design; Risk
PubMed: 30743311
DOI: 10.1002/sim.8115 -
BMC Medical Research Methodology Jul 2017In a random effects meta-analysis model, true treatment effects for each study are routinely assumed to follow a normal distribution. However, normality is a restrictive...
BACKGROUND
In a random effects meta-analysis model, true treatment effects for each study are routinely assumed to follow a normal distribution. However, normality is a restrictive assumption and the misspecification of the random effects distribution may result in a misleading estimate of overall mean for the treatment effect, an inappropriate quantification of heterogeneity across studies and a wrongly symmetric prediction interval.
METHODS
We focus on problems caused by an inappropriate normality assumption of the random effects distribution, and propose a novel random effects meta-analysis model where a Box-Cox transformation is applied to the observed treatment effect estimates. The proposed model aims to normalise an overall distribution of observed treatment effect estimates, which is sum of the within-study sampling distributions and the random effects distribution. When sampling distributions are approximately normal, non-normality in the overall distribution will be mainly due to the random effects distribution, especially when the between-study variation is large relative to the within-study variation. The Box-Cox transformation addresses this flexibly according to the observed departure from normality. We use a Bayesian approach for estimating parameters in the proposed model, and suggest summarising the meta-analysis results by an overall median, an interquartile range and a prediction interval. The model can be applied for any kind of variables once the treatment effect estimate is defined from the variable.
RESULTS
A simulation study suggested that when the overall distribution of treatment effect estimates are skewed, the overall mean and conventional I from the normal random effects model could be inappropriate summaries, and the proposed model helped reduce this issue. We illustrated the proposed model using two examples, which revealed some important differences on summary results, heterogeneity measures and prediction intervals from the normal random effects model.
CONCLUSIONS
The random effects meta-analysis with the Box-Cox transformation may be an important tool for examining robustness of traditional meta-analysis results against skewness on the observed treatment effect estimates. Further critical evaluation of the method is needed.
Topics: Algorithms; Bayes Theorem; Computer Simulation; Humans; Meta-Analysis as Topic; Models, Statistical; Multivariate Analysis; Normal Distribution
PubMed: 28724350
DOI: 10.1186/s12874-017-0376-7 -
PloS One 2022In the case of comparing means of various groups, data exploration and comparison for affecting factors or relative indices would be involved. This process is not only...
In the case of comparing means of various groups, data exploration and comparison for affecting factors or relative indices would be involved. This process is not only complex requiring extensive statistical knowledge and methods, but also challenging for the complex installation of existing tools for users who lack of statistical knowledge and coding experience. Like, the normal distribution and equal variance are crucial premises of parametric statistical analysis. But some studies reported that associated data from various industries violated the normal distribution and equal variance, parametric analysis still involved leading to invalid results. This is owing to that the normal distribution tests and homogeneity of variance test for different variables are time-cost and error-prone, posing an urgent need for an automatic and user-friendly analysis application, not only integrating normal distribution tests and homogeneity of variance test, but also associated the following statistical analysis. To address this, we developed a Shiny/R application, moreThanANOVA, which is an interactive, user-friendly, open-source and cloud-based visualization application to achieve automatic distribution tests, and correlative significance tests, then customize post-hoc analysis based on the considerations to the trade-off of Type I and Type II errors (deployed at https://hanchen.shinyapps.io/moreThanANOVA/). moreThanANOVA enables novice users to perform their complex statistical analyses quickly and credibly with interactive visualization and download publication-ready graphs for further analysis.
Topics: Normal Distribution; Software
PubMed: 35802729
DOI: 10.1371/journal.pone.0271185 -
Biochemia Medica Feb 2020Uncertainty is an inseparable part of all types of measurement. Recently, the International Organization for Standardization (ISO) released a new standard (ISO 20914) on... (Review)
Review
Uncertainty is an inseparable part of all types of measurement. Recently, the International Organization for Standardization (ISO) released a new standard (ISO 20914) on how to calculate measurement uncertainty (MU) in laboratory medicine. This standard can be regarded as the beginning of a new era in laboratory medicine. Measurement uncertainty comprises various components and is used to calculate the total uncertainty. All components must be expressed in standard deviation (SD) and then combined. However, the characteristics of these components are not the same; some are expressed as SD, while others are expressed as a ± b, such as the purity of the reagents. All non-SD variables must be transformed into SD, which requires a detailed knowledge of common statistical distributions used in the calculation of MU. Here, the main statistical distributions used in MU calculation are briefly summarized.
Topics: Humans; Medical Laboratory Science; Statistical Distributions; Uncertainty
PubMed: 32063728
DOI: 10.11613/BM.2020.010101 -
Computational Intelligence and... 2022In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties...
In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating function, moment generating function, index of dispersion, Shannon entropy, Mills ratio, mean residual life function, and associated measures are investigated. All these properties can be expressed in explicit forms. It is found that the new probability mass function can be utilized to model positively skewed data with leptokurtic shape. Moreover, the new discrete distribution is considered a proper tool to model equi- and over-dispersed phenomena with increasing hazard rate function. The distribution parameter is estimated by different six estimation approaches, and the behavior of these methods is explored using the Monte Carlo simulation. Finally, two applications to real life are presented herein to illustrate the flexibility of the new model.
Topics: Computer Simulation; Likelihood Functions; Models, Statistical; Monte Carlo Method; Poisson Distribution; Reproducibility of Results; Statistical Distributions
PubMed: 35463286
DOI: 10.1155/2022/6503670